Chapter 11.6, Problem 19E

To determine

To calculate: the number of permutations for $P{}_1$ .

Answer to Problem 19E

The number of permutations for $P{}_1$ is $9$ .

Explanation of Solution

Given : the expressionis $P{}_1$ .

Formula used:

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

Calculation : tofind the number of permutations , put $n=9$ and $r=1$ , then simplify the result.

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

  $\begin{array}{l}P{}_1=\frac{9!}{\left(9-1\right)!}\text{ [substitute n by 9 and r by 1]}\\ P{}_1=\frac{9·8·7·6·5·4·3·2·1}{8!}\text{ [subtract, expand factorial and divide out common factors]}\\ P{}_1=9\text{ [multiply]}\end{array}$

Hence,The number of permutations for $P{}_1$ is $9$ .