Chapter 13.9, Problem 11PPS

To determine

To calculate: Probability that the first $3$ songs on the CD are selected to play in any order.

Answer to Problem 11PPS

Probability that the first $3$ songs on the CD are selected to play in any order is $\frac{1}{120}$ .

Explanation of Solution

Given information:

Total no of song $=10$ .

Calculation:

At the time of selecting the song randomly, order is not important.

So, the combination will be used.

The number of combinations,

  $=\frac{Thenumberofpermutations}{Thenumberofways}$

As given there are total $10$ no. of songs.

So there are total $10$ choices for selecting the first song.

  $9$ choices for choosing the second song.

So number of permutation,

  $\begin{array}{l}=10\times 9\times 8\\ =720\end{array}$

Thus, there are $\mathrm{3.2.1}$ ways for choosing the songs.

The numbers of Ways that the three songs are chosen to play without repeating a song are as below:

  $\begin{array}{l}C\left(10,3\right)=\frac{720}{\mathrm{3.2.1}}\\ =\frac{720}{6}\\ =120\end{array}$