Chapter 12.6, Problem 17P

There are 100 songs on your music player. In how many different ways can you arrange 20 songs to listen to while exercising?

To determine

Find the number of different ways that you can arrange 20 songs to listen to while exercising.

Answer to Problem 17P

  $P{}_{20}$

Explanation of Solution

Given:

There are 100 songs on your music player.

Formula Used:

  $P{}_r=\frac{n!}{(n-r)!}$

Calculation:

Since you need to arrange 20 songs , so the order of selection matters and select the 20 songs from 100 without replacement. So, the number of different ways that you can arrange 20 songs to listen to while exercising:

  $P{}_{20}=\frac{100!}{(100-20)!}=\frac{100!}{80!}$ .