K Use permutations to solve. In a club with 18 members, how many ways can the club elect a president and a treasurer? Substitute values into the formula for Pr. nPr=
K Use permutations to solve. In a club with 18 members, how many ways can the club elect a president and a treasurer? Substitute values into the formula for Pr. nPr=
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Using Permutations to Solve a Problem**
**Problem Statement:**
In a club with 18 members, how many ways can the club elect a president and a treasurer?
---
**Step to Solve:**
Substitute values into the formula for permutations, denoted as \( _nP_r \):
\[
_nP_r = \frac{n!}{(n-r)!}
\]
Here, \( n \) represents the total number of members, and \( r \) represents the number of positions to fill (2 in this case, for president and treasurer).
---
**Formula Explanation:**
- \( n! \) is the factorial of the total number of members.
- \( (n-r)! \) is the factorial of the difference between the total number of members and the number of positions to fill.
Using this formula, you can calculate the number of ways to choose and arrange the positions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3dbf7f3-2b01-42b1-b2c1-9de501fbe463%2F64ee558c-72b1-47ed-95b5-dae45874861b%2Ftu5vk3j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using Permutations to Solve a Problem**
**Problem Statement:**
In a club with 18 members, how many ways can the club elect a president and a treasurer?
---
**Step to Solve:**
Substitute values into the formula for permutations, denoted as \( _nP_r \):
\[
_nP_r = \frac{n!}{(n-r)!}
\]
Here, \( n \) represents the total number of members, and \( r \) represents the number of positions to fill (2 in this case, for president and treasurer).
---
**Formula Explanation:**
- \( n! \) is the factorial of the total number of members.
- \( (n-r)! \) is the factorial of the difference between the total number of members and the number of positions to fill.
Using this formula, you can calculate the number of ways to choose and arrange the positions.
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