Use permutations to solve. Tim is a huge fan of country music. If Tim has time to listen to only 5 of the 14 songs on an album, how many ways can he listen to the 5 songs? Substitute values into the formula for Pr. nPr= (Type an integer or a decimal.) (...)
Use permutations to solve. Tim is a huge fan of country music. If Tim has time to listen to only 5 of the 14 songs on an album, how many ways can he listen to the 5 songs? Substitute values into the formula for Pr. nPr= (Type an integer or a decimal.) (...)
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 Problem: Selecting Songs**
**Problem Statement:**
Tim is a huge fan of country music. If Tim has time to listen to only 5 of the 14 songs on an album, how many ways can he listen to the 5 songs?
---
**Solution Approach:**
To find the number of ways Tim can listen to 5 songs out of 14, we use permutations since the order of listening matters.
**Permutation Formula:**
\[
^nP_r = \frac{n!}{(n-r)!}
\]
Where:
- \( n \) is the total number of songs,
- \( r \) is the number of songs to be chosen,
- \( n! \) (n factorial) is the product of all positive integers up to \( n \).
**Substitute values into the formula:**
- \( n = 14 \)
- \( r = 5 \)
The formula becomes:
\[
^{14}P_5 = \frac{14!}{(14-5)!}
\]
**Instructions:**
Type an integer or a decimal to solve the permutations.
This approach allows Tim to determine all the possible sequences he can arrange the 5 songs from the given selection of 14.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3dbf7f3-2b01-42b1-b2c1-9de501fbe463%2Fe860d882-8c11-4ef5-b3bf-c139d0dd8ea6%2Fium0pza_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Permutations Problem: Selecting Songs**
**Problem Statement:**
Tim is a huge fan of country music. If Tim has time to listen to only 5 of the 14 songs on an album, how many ways can he listen to the 5 songs?
---
**Solution Approach:**
To find the number of ways Tim can listen to 5 songs out of 14, we use permutations since the order of listening matters.
**Permutation Formula:**
\[
^nP_r = \frac{n!}{(n-r)!}
\]
Where:
- \( n \) is the total number of songs,
- \( r \) is the number of songs to be chosen,
- \( n! \) (n factorial) is the product of all positive integers up to \( n \).
**Substitute values into the formula:**
- \( n = 14 \)
- \( r = 5 \)
The formula becomes:
\[
^{14}P_5 = \frac{14!}{(14-5)!}
\]
**Instructions:**
Type an integer or a decimal to solve the permutations.
This approach allows Tim to determine all the possible sequences he can arrange the 5 songs from the given selection of 14.
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