Chapter 11.6, Problem 21E

To determine

To calculate: the number of permutations for $P{}_5$ .

Answer to Problem 21E

The number of permutations for $P{}_5$ is $6720$ .

Explanation of Solution

Given :, the expressionis $P{}_5$ .

Formula used:

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

Calculation : tofind the number of permutations , put $n=8$ and $r=5$ , then simplify the result.

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

  $\begin{array}{l}P{}_5=\frac{8!}{\left(8-5\right)!}\text{ [subtract n by 8 and r by 5]}\\ P{}_5=\frac{8·7·6·5·4·3·2·1}{3!}\text{ [subtract, expand factorial and divide out common factors]}\\ P{}_5=6720\text{ [multiply]}\end{array}$

Hence,The number of permutations for $P{}_5$ is $6720$ .