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2026-01-01
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2026-02-21
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<p>272 Learners</p>
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<p>305 Learners</p>
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<p>Last updated on<strong>October 22, 2025</strong></p>
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<p>Last updated on<strong>October 22, 2025</strong></p>
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<p>Permutations and combinations are methods used to arrange or select items from a larger set. The key difference lies in whether the order of selection matters.</p>
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<p>Permutations and combinations are methods used to arrange or select items from a larger set. The key difference lies in whether the order of selection matters.</p>
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<h2>What is Permutation?</h2>
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<h2>What is Permutation?</h2>
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<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<p>A<a></a><a>permutation</a>is the<a>number</a>of ways to arrange a<a>set</a>of items in a specific order.</p>
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<p>A<a></a><a>permutation</a>is the<a>number</a>of ways to arrange a<a>set</a>of items in a specific order.</p>
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<p>It is represented as \(^nP_r\), where n is the total number of items and r is the number of items chosen for the arrangement.</p>
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<p>It is represented as \(^nP_r\), where n is the total number of items and r is the number of items chosen for the arrangement.</p>
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<p>The<a>formula</a>to calculate Permutation is:</p>
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<p>The<a>formula</a>to calculate Permutation is:</p>
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<p>\(^nP_r = \frac {n!} {(n - r)!}\)</p>
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<p>\(^nP_r = \frac {n!} {(n - r)!}\)</p>
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<h2>What is Combination?</h2>
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<h2>What is Combination?</h2>
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<p>A<a></a><a>combination</a>is the selection of items from a larger<a>set</a>where the order of selection is not important.</p>
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<p>A<a></a><a>combination</a>is the selection of items from a larger<a>set</a>where the order of selection is not important.</p>
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<p>It is represented by \(^nC_r\), where n is the total number of distinct items and r is the number of items selected.</p>
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<p>It is represented by \(^nC_r\), where n is the total number of distinct items and r is the number of items selected.</p>
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<p>The formula for combination is:</p>
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<p>The formula for combination is:</p>
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<p>\(^nC_r = \frac {n!} {[r! × (n - r)!]}\)</p>
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<p>\(^nC_r = \frac {n!} {[r! × (n - r)!]}\)</p>
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<h2>Difference Between Permutations and Combinations</h2>
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<h2>Difference Between Permutations and Combinations</h2>
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<p>The order of selection of items is the main difference between<a>permutations and combinations</a>. Now we will learn the difference between permutations and combinations in detail. </p>
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<p>The order of selection of items is the main difference between<a>permutations and combinations</a>. Now we will learn the difference between permutations and combinations in detail. </p>
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<p><strong>Permutation</strong></p>
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<p><strong>Permutation</strong></p>
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<p><strong>Combination </strong></p>
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<p><strong>Combination </strong></p>
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<p>A permutation is the number of ways of arranging items in a specific order.</p>
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<p>A permutation is the number of ways of arranging items in a specific order.</p>
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<p>A combination is the total number of possible selections of items from a given set. </p>
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<p>A combination is the total number of possible selections of items from a given set. </p>
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<p>In permutation, the order plays an important role.</p>
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<p>In permutation, the order plays an important role.</p>
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<p>The order of the items is not important for the combination.</p>
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<p>The order of the items is not important for the combination.</p>
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<p>When the items are of different kinds, we use permutations.</p>
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<p>When the items are of different kinds, we use permutations.</p>
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<p>When the items are of a similar kind and when order does not matter, we use combinations.</p>
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<p>When the items are of a similar kind and when order does not matter, we use combinations.</p>
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<p>The possible outcomes of tossing two coins are: {HH, HT, TH, TT}. Here, HT and TH are different, as in order matters.</p>
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<p>The possible outcomes of tossing two coins are: {HH, HT, TH, TT}. Here, HT and TH are different, as in order matters.</p>
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<p>When tossing two coins, the possible outcomes are: {HH, HT, TT}. As order does not matter in combinations, we consider HT and TH as one. </p>
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<p>When tossing two coins, the possible outcomes are: {HH, HT, TT}. As order does not matter in combinations, we consider HT and TH as one. </p>
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<p>Permutation formula: \(^nP_r = \frac {n!} {(n - r)!}\)</p>
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<p>Permutation formula: \(^nP_r = \frac {n!} {(n - r)!}\)</p>
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<p>Combination formula: \(^nC_r = \frac {n!} {[r! × (n - r)!]}\)</p>
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<p>Combination formula: \(^nC_r = \frac {n!} {[r! × (n - r)!]}\)</p>
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<h2>What is the Relation Between Permutation and Combination?</h2>
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<h2>What is the Relation Between Permutation and Combination?</h2>
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<p>By<a>comparing</a>the formulas of permutation and combination, let’s understand the relationship between permutation and combination.</p>
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<p>By<a>comparing</a>the formulas of permutation and combination, let’s understand the relationship between permutation and combination.</p>
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<p>When selecting and arranging r items from n, we can express the permutation as the<a>product</a>of r! And the combination of those r items.</p>
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<p>When selecting and arranging r items from n, we can express the permutation as the<a>product</a>of r! And the combination of those r items.</p>
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<p>\(^nP_r = \frac {n!} {(n - r)!}\)</p>
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<p>\(^nP_r = \frac {n!} {(n - r)!}\)</p>
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<p>We can rewrite it as:</p>
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<p>We can rewrite it as:</p>
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<p>\(^nP_r = \frac {(r! × n!)}{[r! × (n - r)! ]}\)</p>
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<p>\(^nP_r = \frac {(r! × n!)}{[r! × (n - r)! ]}\)</p>
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<p>\(^nP_r = r! ×\ ^nC_r \)</p>
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<p>\(^nP_r = r! ×\ ^nC_r \)</p>
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<p>Thus, the number of permutations is the product of the number of combinations and the ways to arrange the selected items (r!).</p>
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<p>Thus, the number of permutations is the product of the number of combinations and the ways to arrange the selected items (r!).</p>
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<h2>Tips and Tricks to Master Difference Between Permutations and Combinations</h2>
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<h2>Tips and Tricks to Master Difference Between Permutations and Combinations</h2>
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<p>Here are some fun, easy-to-remember tips and tricks to help students and parents master the difference between permutations and combinations </p>
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<p>Here are some fun, easy-to-remember tips and tricks to help students and parents master the difference between permutations and combinations </p>
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<ol><li><p>Remember the golden rule that, while finding the permutation, position matters. On the other hand, to find the combination, position doesn’t matter. </p>
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<ol><li><p>Remember the golden rule that, while finding the permutation, position matters. On the other hand, to find the combination, position doesn’t matter. </p>
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</li>
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</li>
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<li><p>You can help yourself before solving a problem by always asking if the order makes a difference. If they do, then it is a permutation problem and if it does not, then we have to find the combinations. </p>
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<li><p>You can help yourself before solving a problem by always asking if the order makes a difference. If they do, then it is a permutation problem and if it does not, then we have to find the combinations. </p>
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</li>
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</li>
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<li><p>The easiest way to identify these formulas is to remember that, if the formula includes r! in the<a>denominator</a>, it’s a combination, because it removes duplicate orders. </p>
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<li><p>The easiest way to identify these formulas is to remember that, if the formula includes r! in the<a>denominator</a>, it’s a combination, because it removes duplicate orders. </p>
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</li>
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</li>
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<li><p>If you are confused about permutations and combinations in the middle of a<a>question</a>, then remember that if we are arranging people, numbers, or letters, we must use permutation. On the other hand, if we are choosing people, numbers, or letters, then we must use combination. </p>
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<li><p>If you are confused about permutations and combinations in the middle of a<a>question</a>, then remember that if we are arranging people, numbers, or letters, we must use permutation. On the other hand, if we are choosing people, numbers, or letters, then we must use combination. </p>
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</li>
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</li>
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<li><p>To make your calculation faster while dealing with permutations, try counting ways to seat family members at dinner. For combinations, count ways to select friends for a group photo.</p>
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<li><p>To make your calculation faster while dealing with permutations, try counting ways to seat family members at dinner. For combinations, count ways to select friends for a group photo.</p>
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</li>
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</li>
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</ol><h2>Common Mistakes and How to Avoid Them in Difference Between Permutations and Combinations</h2>
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</ol><h2>Common Mistakes and How to Avoid Them in Difference Between Permutations and Combinations</h2>
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<p>Students often confuse permutations and combinations, leading to errors. So we will be learning some common mistakes and ways to avoid them.</p>
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<p>Students often confuse permutations and combinations, leading to errors. So we will be learning some common mistakes and ways to avoid them.</p>
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<h2>Real-World Applications of Difference Between Permutations and Combinations</h2>
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<h2>Real-World Applications of Difference Between Permutations and Combinations</h2>
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<p>In real life, we use permutations and combinations from creating passwords to scheduling events. In this section, we will learn a few applications of the difference between permutations and combinations.</p>
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<p>In real life, we use permutations and combinations from creating passwords to scheduling events. In this section, we will learn a few applications of the difference between permutations and combinations.</p>
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<ul><li>We use permutations to generate passwords, as the order of characters matters in passwords. The order of digits or letters changes the password completely. </li>
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<ul><li>We use permutations to generate passwords, as the order of characters matters in passwords. The order of digits or letters changes the password completely. </li>
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<li>We use permutations in cybersecurity and cryptography to create unique codes and passwords, as the order of characters is important. </li>
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<li>We use permutations in cybersecurity and cryptography to create unique codes and passwords, as the order of characters is important. </li>
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<li>When you pick members for a team, it doesn’t matter in which order they are selected. Because selection matters, not order, it’s a combination. For example, forming school committees or project groups </li>
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<li>When you pick members for a team, it doesn’t matter in which order they are selected. Because selection matters, not order, it’s a combination. For example, forming school committees or project groups </li>
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<li>When choosing pizza toppings, the order doesn’t matter; cheese, mushroom, and corn is the same as corn, cheese, and mushroom. Since the combination is what matters, not order, this is a combination. </li>
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<li>When choosing pizza toppings, the order doesn’t matter; cheese, mushroom, and corn is the same as corn, cheese, and mushroom. Since the combination is what matters, not order, this is a combination. </li>
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<li>The permutations and combinations are used to assign phone numbers, city codes, car numbers, and telephone codes, as the order of the characters is important.</li>
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<li>The permutations and combinations are used to assign phone numbers, city codes, car numbers, and telephone codes, as the order of the characters is important.</li>
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</ul><h3>Problem 1</h3>
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</ul><h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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<p>From a set of 5 different books, in how many ways can you select 3 books and arrange them on a shelf?</p>
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<p>From a set of 5 different books, in how many ways can you select 3 books and arrange them on a shelf?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The number of ways to choose 3 books is 10. The ways of arranging 3 books from a set of 5 are 60.</p>
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<p>The number of ways to choose 3 books is 10. The ways of arranging 3 books from a set of 5 are 60.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The number of ways to select books: \(^nC_r = \frac {n!} {[r! × (n - r)!]}\)</p>
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<p>The number of ways to select books: \(^nC_r = \frac {n!} {[r! × (n - r)!]}\)</p>
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<p>Here, n = 5 and r = 3</p>
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<p>Here, n = 5 and r = 3</p>
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<p>\(^5C_3 = \frac {5!} {[3! × (5 - 3)!]}\\ ^5C_3= \frac {5!} {[3! × 2!]}\\ ^5C_3= \frac {(5× 4× 3! )}{(3! ×2!)}\\ ^5C_3= \frac {(5× 4 )}{2!}\\ ^5C_3= \frac {5×4}{2×1}\\ ^5C_3=\frac {20}{2}\\ ^5C_3= 10\)</p>
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<p>\(^5C_3 = \frac {5!} {[3! × (5 - 3)!]}\\ ^5C_3= \frac {5!} {[3! × 2!]}\\ ^5C_3= \frac {(5× 4× 3! )}{(3! ×2!)}\\ ^5C_3= \frac {(5× 4 )}{2!}\\ ^5C_3= \frac {5×4}{2×1}\\ ^5C_3=\frac {20}{2}\\ ^5C_3= 10\)</p>
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<p>To find the ways of arranging 3 books on a shelf, we calculate the permutations: </p>
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<p>To find the ways of arranging 3 books on a shelf, we calculate the permutations: </p>
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<p>\(^nP_r = \frac {n!} {(n - r)!}\)</p>
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<p>\(^nP_r = \frac {n!} {(n - r)!}\)</p>
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<p>Here, n = 5 and r = 3</p>
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<p>Here, n = 5 and r = 3</p>
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<p>\(^nP_r =\frac {5!} {(5 - 3)!}\\ ^5P_3= \frac {5!} {2!} \\ ^5P_3= \frac {(5 × 4 × 3 × 2!)} { 2!}\\ ^5P_3= 5 × 4 × 3 \\ ^5P_3= 60\)</p>
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<p>\(^nP_r =\frac {5!} {(5 - 3)!}\\ ^5P_3= \frac {5!} {2!} \\ ^5P_3= \frac {(5 × 4 × 3 × 2!)} { 2!}\\ ^5P_3= 5 × 4 × 3 \\ ^5P_3= 60\)</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>In how many ways can you arrange 4 out of 7 different letters?</p>
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<p>In how many ways can you arrange 4 out of 7 different letters?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>We can arrange the letters in 840 ways.</p>
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<p>We can arrange the letters in 840 ways.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the ways of arranging 4 out of 7 different letters, we use the permutation formula.</p>
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<p>To find the ways of arranging 4 out of 7 different letters, we use the permutation formula.</p>
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<p>\(^nP_r = \frac {n!} {(n - r)!}\)</p>
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<p>\(^nP_r = \frac {n!} {(n - r)!}\)</p>
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<p>Here, n = 7 and r = 4</p>
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<p>Here, n = 7 and r = 4</p>
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<p>\(nPr = \frac {7!}{(7 - 4)!}\\ ^7P_4 = \frac {7!}{3!} \\ ^7P_4= \frac {(7 × 6 × 5 × 4 × 3!)}{3!}\\ ^7P_4= 7 × 6 × 5 × 4 \\ ^7P_4= 840\)</p>
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<p>\(nPr = \frac {7!}{(7 - 4)!}\\ ^7P_4 = \frac {7!}{3!} \\ ^7P_4= \frac {(7 × 6 × 5 × 4 × 3!)}{3!}\\ ^7P_4= 7 × 6 × 5 × 4 \\ ^7P_4= 840\)</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>How many ways can you form a team of 4 from 10 players?</p>
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<p>How many ways can you form a team of 4 from 10 players?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The number of ways you can form a team of 4 from 10 players is 210.</p>
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<p>The number of ways you can form a team of 4 from 10 players is 210.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find how many ways we can form a team of 4 people from a group of 10, we use the combination formula</p>
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<p>To find how many ways we can form a team of 4 people from a group of 10, we use the combination formula</p>
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<p>\(^nC_r = \frac {n!} {[r! × (n - r)!]}\)</p>
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<p>\(^nC_r = \frac {n!} {[r! × (n - r)!]}\)</p>
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<p>Where n = 10 and r = 4</p>
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<p>Where n = 10 and r = 4</p>
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<p>\(C(10, 4) = \frac {10! } {[4! × (10 - 4)!]}\\ ^{10}C_4 = \frac {10!}{(4! × 6!)}\\ ^{10}C_4= \frac {(10 × 9 × 8 × 7 × 6!)}{(4! × 6!)}\\ ^{10}C_4= \frac {(10 × 9 × 8 × 7)} {(4 × 3 × 2 × 1)}\\ ^{10}C_4= \frac {5040}{24}\\ ^{10}C_4= 210\)</p>
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<p>\(C(10, 4) = \frac {10! } {[4! × (10 - 4)!]}\\ ^{10}C_4 = \frac {10!}{(4! × 6!)}\\ ^{10}C_4= \frac {(10 × 9 × 8 × 7 × 6!)}{(4! × 6!)}\\ ^{10}C_4= \frac {(10 × 9 × 8 × 7)} {(4 × 3 × 2 × 1)}\\ ^{10}C_4= \frac {5040}{24}\\ ^{10}C_4= 210\)</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>In how many ways can 5 people be arranged in a line from a group of 9?</p>
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<p>In how many ways can 5 people be arranged in a line from a group of 9?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>We can arrange them in 15120 ways</p>
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<p>We can arrange them in 15120 ways</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the ways to arrange 5 people in a line from a group of 9, we use the permutation formula</p>
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<p>To find the ways to arrange 5 people in a line from a group of 9, we use the permutation formula</p>
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<p>\(^nP_r = \frac {n!} {(n - r)!}\)</p>
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<p>\(^nP_r = \frac {n!} {(n - r)!}\)</p>
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<p>Here, n = 9 and r = 5</p>
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<p>Here, n = 9 and r = 5</p>
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<p>\(^9P_5 = \frac {9!} {(9 - 5)!}\\ ^9P_5= \frac {9!} {4!}\\ ^9P_5= \frac {(9 × 8 × 7 × 6 × 5 × 4!)} {4!}\\ ^9P_5= 15120\)</p>
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<p>\(^9P_5 = \frac {9!} {(9 - 5)!}\\ ^9P_5= \frac {9!} {4!}\\ ^9P_5= \frac {(9 × 8 × 7 × 6 × 5 × 4!)} {4!}\\ ^9P_5= 15120\)</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>Out of 7 runners, how many ways can you select 3 to join a relay team?</p>
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<p>Out of 7 runners, how many ways can you select 3 to join a relay team?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>In 35 ways, we can select the relay team</p>
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<p>In 35 ways, we can select the relay team</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the number of ways to select 3 runners to join a relay team, we find the combination</p>
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<p>To find the number of ways to select 3 runners to join a relay team, we find the combination</p>
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<p>\(^nC_r = \frac {n!} {[r! × (n - r)!]}\)</p>
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<p>\(^nC_r = \frac {n!} {[r! × (n - r)!]}\)</p>
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<p>Here, n = 7 and r = 3</p>
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<p>Here, n = 7 and r = 3</p>
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<p>\(C(7,3) = \frac {7! }{ [3! × (7 - 3)!]}\\ ^7C_3= \frac {7!}{[3! × (7 - 3)!]}\\ ^7C_3= \frac {7! }{(3! × 4!)}\\ ^7C_3= \frac {(7 × 6 × 5 × 4!)}{(4! × 3 × 2 × 1)}\\ ^7C_3= \frac {(7 × 6 × 5)}{(3 × 2 × 1)}\\ ^7C_3= 35\)</p>
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<p>\(C(7,3) = \frac {7! }{ [3! × (7 - 3)!]}\\ ^7C_3= \frac {7!}{[3! × (7 - 3)!]}\\ ^7C_3= \frac {7! }{(3! × 4!)}\\ ^7C_3= \frac {(7 × 6 × 5 × 4!)}{(4! × 3 × 2 × 1)}\\ ^7C_3= \frac {(7 × 6 × 5)}{(3 × 2 × 1)}\\ ^7C_3= 35\)</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Difference Between Permutations and Combinations</h2>
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<h2>FAQs on Difference Between Permutations and Combinations</h2>
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<h3>1.What is the main difference between permutations and combinations?</h3>
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<h3>1.What is the main difference between permutations and combinations?</h3>
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<p>Permutations are the number of ways to arrange items, and combinations are the number of ways to select items. The main difference between permutations and combinations is that in permutations, the order matters, whereas in combinations, the order does not matter. </p>
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<p>Permutations are the number of ways to arrange items, and combinations are the number of ways to select items. The main difference between permutations and combinations is that in permutations, the order matters, whereas in combinations, the order does not matter. </p>
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<h3>2.What is the formula for a combination?</h3>
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<h3>2.What is the formula for a combination?</h3>
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<p>The formula for combination is: nCr = n! / [r! × (n - r)!]</p>
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<p>The formula for combination is: nCr = n! / [r! × (n - r)!]</p>
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<h3>3.What is the formula for permutations?</h3>
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<h3>3.What is the formula for permutations?</h3>
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<p>The formula for permutation is: nPr = n! / (n - r)! </p>
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<p>The formula for permutation is: nPr = n! / (n - r)! </p>
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<h3>4.How many combinations of 2 out of 5?</h3>
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<h3>4.How many combinations of 2 out of 5?</h3>
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<p>The formula to find the combination is: nCr = n! / [r! × (n - r)!] = C(5, 2) = 5! / (2! × 3! ) = 10. </p>
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<p>The formula to find the combination is: nCr = n! / [r! × (n - r)!] = C(5, 2) = 5! / (2! × 3! ) = 10. </p>
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<h3>5.What is 2!?</h3>
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<h3>5.What is 2!?</h3>
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<p>The value of 2! is 2, as 2! = 2 × 1 = 2. </p>
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<p>The value of 2! is 2, as 2! = 2 × 1 = 2. </p>
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<h3>6.What is the easiest way to explain permutations and combinations to my child?</h3>
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<h3>6.What is the easiest way to explain permutations and combinations to my child?</h3>
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<p>Tell them that "permutation is when order matters." It means that we are arranging things. Combination is when order doesn’t matter, where we are choosing things. Give them some real-life examples to make them live the situations.</p>
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<p>Tell them that "permutation is when order matters." It means that we are arranging things. Combination is when order doesn’t matter, where we are choosing things. Give them some real-life examples to make them live the situations.</p>
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<h3>7.How can I help my child remember which is which?</h3>
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<h3>7.How can I help my child remember which is which?</h3>
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<p>Ask them to use this memory trick:</p>
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<p>Ask them to use this memory trick:</p>
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<p>P in permutation stands for "position", where order matters.</p>
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<p>P in permutation stands for "position", where order matters.</p>
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<p>C in combination stands for "choose", where order doesn’t matter.</p>
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<p>C in combination stands for "choose", where order doesn’t matter.</p>
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<h3>8.Why is it important for my kid to learn this concept?</h3>
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<h3>8.Why is it important for my kid to learn this concept?</h3>
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<p>Understanding permutations and combinations improves logical and analytical thinking,<a>probability</a>understanding, decision-making and counting skills. It’s also used in coding,<a>data</a>science, and AI. So it builds long-<a>term</a><a>math</a>confidence.</p>
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<p>Understanding permutations and combinations improves logical and analytical thinking,<a>probability</a>understanding, decision-making and counting skills. It’s also used in coding,<a>data</a>science, and AI. So it builds long-<a>term</a><a>math</a>confidence.</p>
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<h2>Jaipreet Kour Wazir</h2>
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<h2>Jaipreet Kour Wazir</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref</p>
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<p>Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: She compares datasets to puzzle games-the more you play with them, the clearer the picture becomes!</p>
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<p>: She compares datasets to puzzle games-the more you play with them, the clearer the picture becomes!</p>