Find the number of permutations. 7 objects taken 4 at a time There are permutations.
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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Question
![**Problem Statement:**
*Find the number of permutations.*
**Details:**
*7 objects taken 4 at a time*
---
**Answer Field:**
*There are [ ] permutations.*
---
**Explanation:**
This problem requires finding the number of permutations of 7 distinct objects taken 4 at a time. To find the number of permutations, use the formula for permutations:
\[ P(n, r) = \frac{n!}{(n-r)!} \]
In this case, \( n = 7 \) and \( r = 4 \).
Calculate as follows:
\[ P(7, 4) = \frac{7!}{(7-4)!} = \frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} = 7 \times 6 \times 5 \times 4 = 840 \]
Therefore, there are 840 permutations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35ad263b-c31f-4196-aa81-a0a5a787610e%2Fc2843cc3-a3be-46d8-998c-976177c9c72e%2Fv1mve8x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
*Find the number of permutations.*
**Details:**
*7 objects taken 4 at a time*
---
**Answer Field:**
*There are [ ] permutations.*
---
**Explanation:**
This problem requires finding the number of permutations of 7 distinct objects taken 4 at a time. To find the number of permutations, use the formula for permutations:
\[ P(n, r) = \frac{n!}{(n-r)!} \]
In this case, \( n = 7 \) and \( r = 4 \).
Calculate as follows:
\[ P(7, 4) = \frac{7!}{(7-4)!} = \frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} = 7 \times 6 \times 5 \times 4 = 840 \]
Therefore, there are 840 permutations.
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