11, = 0 10P4 = 0 Th 3 Evaluate 11C7 and 10P4- (If necessary, consult a list of formulas.) X 1 3 4 = 5 6
11, = 0 10P4 = 0 Th 3 Evaluate 11C7 and 10P4- (If necessary, consult a list of formulas.) X 1 3 4 = 5 6
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please show me how to solve this problem.
![**Evaluate Combinations and Permutations**
Evaluate \( \binom{11}{7} \) and \( {}^{10}P_4 \).
(If necessary, consult a list of formulas.)
\[
\binom{11}{7} = \boxed{}
\]
\[
{}^{10}P_4 = \boxed{}
\]
**Explanation:**
- **Combination \( \binom{n}{r} \):** Represents the number of ways to choose \( r \) items from \( n \) items without regard to order. The formula is \( \binom{n}{r} = \frac{n!}{r!(n-r)!} \).
- **Permutation \( {}^{n}P_{r} \):** Represents the number of ways to arrange \( r \) items from \( n \) items with regard to order. The formula is \( {}^{n}P_{r} = \frac{n!}{(n-r)!} \).
Complete the calculations using these formulas.
**Solutions:**
1. **Combination:**
- Calculate \( \binom{11}{7} \).
2. **Permutation:**
- Calculate \( {}^{10}P_{4} \).
**Instructions:**
- Use the dropdown boxes to select or enter your answers.
- Click "Continue" to proceed with the exercise.
**Notes:**
Understanding combinations and permutations is key in probability and statistics, where order and selection are analyzed in different contexts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde56390e-d2c8-45f5-9f83-c95fbb4c473e%2Ff9358051-259a-430f-b228-f70e19ba997f%2Fd0yio1h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Evaluate Combinations and Permutations**
Evaluate \( \binom{11}{7} \) and \( {}^{10}P_4 \).
(If necessary, consult a list of formulas.)
\[
\binom{11}{7} = \boxed{}
\]
\[
{}^{10}P_4 = \boxed{}
\]
**Explanation:**
- **Combination \( \binom{n}{r} \):** Represents the number of ways to choose \( r \) items from \( n \) items without regard to order. The formula is \( \binom{n}{r} = \frac{n!}{r!(n-r)!} \).
- **Permutation \( {}^{n}P_{r} \):** Represents the number of ways to arrange \( r \) items from \( n \) items with regard to order. The formula is \( {}^{n}P_{r} = \frac{n!}{(n-r)!} \).
Complete the calculations using these formulas.
**Solutions:**
1. **Combination:**
- Calculate \( \binom{11}{7} \).
2. **Permutation:**
- Calculate \( {}^{10}P_{4} \).
**Instructions:**
- Use the dropdown boxes to select or enter your answers.
- Click "Continue" to proceed with the exercise.
**Notes:**
Understanding combinations and permutations is key in probability and statistics, where order and selection are analyzed in different contexts.
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