Find the number of permutations. Twelve objects taken seven at a time There are permutations.
Find the number of permutations. Twelve objects taken seven 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
![**Find the Number of Permutations**
Twelve objects are taken seven at a time.
**Question:**
How many permutations are there?
[Input Box] There are ___ permutations.
---
**Explanation:**
Permutations refer to the different arrangements of a set of objects. Here, we are considering the permutations for selecting and arranging seven objects from a total of twelve. The general formula for permutations is given by:
\[ P(n, r) = \frac{n!}{(n-r)!} \]
Where:
- \( n \) is the total number of objects.
- \( r \) is the number of objects to choose.
- \( n! \) (n factorial) is the product of all positive integers up to \( n \).
In this problem:
- \( n = 12 \)
- \( r = 7 \)
Applying the formula, the permutations can be calculated to find the number of unique arrangements possible.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35ad263b-c31f-4196-aa81-a0a5a787610e%2Fb21f453e-9423-4d78-832d-19032808b3d6%2Fhhzi9ln_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the Number of Permutations**
Twelve objects are taken seven at a time.
**Question:**
How many permutations are there?
[Input Box] There are ___ permutations.
---
**Explanation:**
Permutations refer to the different arrangements of a set of objects. Here, we are considering the permutations for selecting and arranging seven objects from a total of twelve. The general formula for permutations is given by:
\[ P(n, r) = \frac{n!}{(n-r)!} \]
Where:
- \( n \) is the total number of objects.
- \( r \) is the number of objects to choose.
- \( n! \) (n factorial) is the product of all positive integers up to \( n \).
In this problem:
- \( n = 12 \)
- \( r = 7 \)
Applying the formula, the permutations can be calculated to find the number of unique arrangements possible.
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