Evaluate 10C4 and „P4. C = 10 4 44 = ||
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52974bc8-a4de-4d42-883f-f9f7c766178f%2Ffa9dd1ed-18af-46da-9d6e-ea4704b1ddb9%2F80610dr_processed.jpeg&w=3840&q=75)
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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