Chapter 11.6, Problem 49E

To determine

To calculate: the number of possible orders playing the $4$ CDs.

Answer to Problem 49E

the possible orders for playing the $4$ CDs is $\frac{12!}{8!}$ .

Explanation of Solution

Given :

Total CDs = $12$

Choose CDs = $4$

Formula used:

  $P{}_r=\frac{n!}{\left(n-r\right)!}$

Calculation : tofind the number of possible orders for playing $4$ CDs, put $n=12$ and $r=4$ in the formula. Because we have to chose 4 CDs among the 12 CDs.

  $\begin{array}{l}P{}_r=\frac{n!}{\left(n-r\right)!}\\ P{}_4=\frac{12!}{\left(12-4\right)!}\text{ [substitue n by 12 and r by 4]}\\ P{}_4=\frac{12!}{8!}\text{ [subtract]}\end{array}$

Hence,the possible orders for playing the $4$ CDs is $\frac{12!}{8!}$ .