Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**Title: Permutations, Combinations, and License Plate Problem** **1. Tree Diagram for Arrangements** Use a tree diagram to list all possible arrangements of the letters \(a\), \(b\), and \(c\). **2. License Plate Combinations** If a license plate consists of 3 letters followed by 3 digits, how many license plates are possible if the first letter cannot be \(O\) or \(I\)? **Evaluate the Following Permutations and Combinations:** 4. \( P(7, 5) \) 5. \( P(6, 4) \) 6. \( P(100, 2) \) 7. \( C(50, 2) \) 8. \( C(7, 4) \) 9. \( C(13, 11) \) **Explanation:** - **Permutations** \( P(n, r) \) represent the number of ways to arrange \( r \) elements out of a set of \( n \) elements. - **Combinations** \( C(n, r) \) represent the number of ways to choose \( r \) elements from a set of \( n \) elements without regard to the order. This exercise involves understanding the concept of permutations and combinations and applying them to solve real-world problems such as determining the number of unique license plates that can be created under certain constraints.
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Transcribed Image Text:**Title: Permutations, Combinations, and License Plate Problem** **1. Tree Diagram for Arrangements** Use a tree diagram to list all possible arrangements of the letters \(a\), \(b\), and \(c\). **2. License Plate Combinations** If a license plate consists of 3 letters followed by 3 digits, how many license plates are possible if the first letter cannot be \(O\) or \(I\)? **Evaluate the Following Permutations and Combinations:** 4. \( P(7, 5) \) 5. \( P(6, 4) \) 6. \( P(100, 2) \) 7. \( C(50, 2) \) 8. \( C(7, 4) \) 9. \( C(13, 11) \) **Explanation:** - **Permutations** \( P(n, r) \) represent the number of ways to arrange \( r \) elements out of a set of \( n \) elements. - **Combinations** \( C(n, r) \) represent the number of ways to choose \( r \) elements from a set of \( n \) elements without regard to the order. This exercise involves understanding the concept of permutations and combinations and applying them to solve real-world problems such as determining the number of unique license plates that can be created under certain constraints.
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