Evaluate the expression 9Pe. 9Ps =O
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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Question
8:
![**Permutations: Evaluating \( ^9P_6 \)**
---
**Problem Statement:**
Evaluate the expression \( ^9P_6 \).
---
**Solution Explanation:**
The expression \( ^9P_6 \) represents the number of permutations of 9 items taken 6 at a time. The formula for permutations is:
\[
^nP_r = \frac{n!}{(n-r)!}
\]
In this case, \( n = 9 \) and \( r = 6 \). Therefore, the expression becomes:
\[
^9P_6 = \frac{9!}{(9-6)!} = \frac{9!}{3!}
\]
**Step-by-Step Calculation:**
1. Calculate \( 9! \) (9 factorial):
\[
9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 362,880
\]
2. Calculate \( 3! \) (3 factorial):
\[
3! = 3 \times 2 \times 1 = 6
\]
3. Divide the results:
\[
^9P_6 = \frac{362,880}{6} = 60,480
\]
**Final Answer:**
The value of \( ^9P_6 \) is \( 60,480 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0615f7c-3e91-45ec-8ebd-43a498fc758f%2F7521c1dc-796f-4800-af04-3791d3c4a471%2Fduwp51p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Permutations: Evaluating \( ^9P_6 \)**
---
**Problem Statement:**
Evaluate the expression \( ^9P_6 \).
---
**Solution Explanation:**
The expression \( ^9P_6 \) represents the number of permutations of 9 items taken 6 at a time. The formula for permutations is:
\[
^nP_r = \frac{n!}{(n-r)!}
\]
In this case, \( n = 9 \) and \( r = 6 \). Therefore, the expression becomes:
\[
^9P_6 = \frac{9!}{(9-6)!} = \frac{9!}{3!}
\]
**Step-by-Step Calculation:**
1. Calculate \( 9! \) (9 factorial):
\[
9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 362,880
\]
2. Calculate \( 3! \) (3 factorial):
\[
3! = 3 \times 2 \times 1 = 6
\]
3. Divide the results:
\[
^9P_6 = \frac{362,880}{6} = 60,480
\]
**Final Answer:**
The value of \( ^9P_6 \) is \( 60,480 \).
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