Chapter 11.6, Problem 22E

To determine

To calculate: the number of permutations for $P{}_6$ .

Answer to Problem 22E

The number of permutations for $P{}_6$ is $720$ .

Explanation of Solution

Given : the expressionis $P{}_6$ .

Formula used:

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

Calculation : tofind the number of permutations , put $n=6$ and $r=6$ , then simplify the result.

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

  $\begin{array}{l}P{}_6=\frac{6!}{\left(6-6\right)!}\text{ [subtitute n by 6 and r by 6]}\\ P{}_6=\frac{6·5·4·3·2·1}{0!}\text{ [subtract, expand factorial and divide common factors]}\\ P{}_6=720\text{ [multiply]}\end{array}$

Hence,The number of permutations for $P{}_6$ is $720$ .