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Evaluate 10C4 and „P4. C = 10 4 44 = ||

Evaluate 10C4 and „P4. C = 10 4 44 = ||

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Title:** Evaluating Combinations and Permutations **Instructions:** Evaluate \( ^{10}C_4 \) and \( ^4P_4 \). **Boxed Section:** - \( ^{10}C_4 = \) [Input Box] - \( ^4P_4 = \) [Input Box] **Icons Below the Box:** - An "X" icon, possibly to clear the input. - A circular arrow, likely indicating a reset or refresh option. - A question mark, probably for help or additional information. **Explanation:** 1. **Combinations (\( ^nC_r \))**: This represents the number of ways to choose \( r \) elements from a set of \( n \) elements without regard to order. It is calculated as: \[ ^nC_r = \frac{n!}{r!(n-r)!} \] 2. **Permutations (\( ^nP_r \))**: This represents the number of ways to choose \( r \) elements from a set of \( n \) elements with regard to order. It is calculated as: \[ ^nP_r = \frac{n!}{(n-r)!} \] In this exercise, calculate \( ^{10}C_4 \) using the combinations formula, and \( ^4P_4 \) using the permutations formula. Enter your answers in the respective input boxes.
Transcribed Image Text:**Title:** Evaluating Combinations and Permutations **Instructions:** Evaluate \( ^{10}C_4 \) and \( ^4P_4 \). **Boxed Section:** - \( ^{10}C_4 = \) [Input Box] - \( ^4P_4 = \) [Input Box] **Icons Below the Box:** - An "X" icon, possibly to clear the input. - A circular arrow, likely indicating a reset or refresh option. - A question mark, probably for help or additional information. **Explanation:** 1. **Combinations (\( ^nC_r \))**: This represents the number of ways to choose \( r \) elements from a set of \( n \) elements without regard to order. It is calculated as: \[ ^nC_r = \frac{n!}{r!(n-r)!} \] 2. **Permutations (\( ^nP_r \))**: This represents the number of ways to choose \( r \) elements from a set of \( n \) elements with regard to order. It is calculated as: \[ ^nP_r = \frac{n!}{(n-r)!} \] In this exercise, calculate \( ^{10}C_4 \) using the combinations formula, and \( ^4P_4 \) using the permutations formula. Enter your answers in the respective input boxes.
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