Chapter 11.6, Problem 18E

To determine

To calculate: the number of permutations for $P{}_4$ .

Answer to Problem 18E

The number of permutations for $P{}_4$ is $120$ .

Explanation of Solution

Given : the expressionis $P{}_4$ .

Formula used:

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

Calculation : tofind the number of permutations , put $n=5$ and $r=4$ , then simplify the result.

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

  $\begin{array}{l}P{}_4=\frac{5!}{\left(5-4\right)!}\text{ [substitue n by 5 and r by 4]}\\ P{}_4=\frac{5·4·3·2·1}{1!}\text{ [subtract, expand factorial]}\\ P{}_4=\frac{120}{1}\text{ [multiply]}\\ P{}_4=120\text{ [divide]}\end{array}$

Hence,The number of permutations for

$P{}_4$ is $120$ .