Chapter 13.2, Problem 19E

To determine

To find: the total ways in that the CDs can be arranged in display window.

Answer to Problem 19E

There are total $126$ ways for arraigning the CDs in display window.

Explanation of Solution

Given information:

There are five identical country CDs and four identical rap CDs are to be placed in a display window.

The number of different permutations of $n$ things in which $p$ are one of kind and $q$ are another one, then they can be taken at a time, is represented as $\frac{n!}{p!\times q!}$ .

As the identical country CDs are five and identical rap CDs are 4, then the sum of the total CDs is $5+4=9$ .

Here, $9$ is the value of $n$ , $p$ is 5, and $q$ is 4.

Substitute $9$ for $n$ , 5 for $p$ , and 4 for $q$ in the formula $\frac{n!}{p!\times q!}$ to find the total ways.

  $\begin{array}{c}\frac{n!}{p!\times q!}=\frac{9!}{5!\times 4!}\\ =\frac{9\times 8\times 7\times 6\times 5!}{5!\times 4\times 3\times 2}\\ =9\times 7\times 2\\ =126\end{array}$

Therefore, there are total $126$ ways for arraigning the CDs in display window.