Use permutations to solve. The student activity club at the college has 39 members. In how many different ways can the club select a president, a vice president, a treasurer, and a secretary? Substitute values into the formula for npr. nPr= C
Use permutations to solve. The student activity club at the college has 39 members. In how many different ways can the club select a president, a vice president, a treasurer, and a secretary? Substitute values into the formula for npr. nPr= C
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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![**Permutations in Selection of Club Officers**
**Problem:**
The student activity club at the college has 39 members. In how many different ways can the club select a president, a vice president, a treasurer, and a secretary?
**Solution Using Permutations:**
We will use permutations to solve this problem by substituting values into the formula for \( nP_r \).
**Permutation Formula:**
\[
nP_r = \frac{n!}{(n-r)!}
\]
Here, \( n \) represents the total number of members, and \( r \) represents the number of positions to fill.
**Given Values:**
- Total members, \( n = 39 \)
- Positions to fill, \( r = 4 \) (president, vice president, treasurer, secretary)
**Substitution:**
\[
nP_r = \frac{39!}{(39-4)!}
\]
This formula will calculate the number of different ways the club can select four officers from the 39 members.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3dbf7f3-2b01-42b1-b2c1-9de501fbe463%2Fc226aa03-3fe0-4af9-b0ea-e6c3af2ef61e%2Fqbl3w88_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Permutations in Selection of Club Officers**
**Problem:**
The student activity club at the college has 39 members. In how many different ways can the club select a president, a vice president, a treasurer, and a secretary?
**Solution Using Permutations:**
We will use permutations to solve this problem by substituting values into the formula for \( nP_r \).
**Permutation Formula:**
\[
nP_r = \frac{n!}{(n-r)!}
\]
Here, \( n \) represents the total number of members, and \( r \) represents the number of positions to fill.
**Given Values:**
- Total members, \( n = 39 \)
- Positions to fill, \( r = 4 \) (president, vice president, treasurer, secretary)
**Substitution:**
\[
nP_r = \frac{39!}{(39-4)!}
\]
This formula will calculate the number of different ways the club can select four officers from the 39 members.
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