Chapter 11.6, Problem 3E

To determine

To calculate:the number of permutations for $P{}_3$ .

Answer to Problem 3E

The number of permutations for $P{}_3$ is $60$ .

Explanation of Solution

Given : the expressionis $P{}_3$ .

Formula used:

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

Calculation : tofind the number of permutations , put $n=5$ and $r=3$ , then simplify the result.

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

  $\begin{array}{l}P{}_3=\frac{5!}{\left(5-3\right)!}\text{ [substitue n by 5 and r by 3]}\\ P{}_3=\frac{5·4·3·2·1}{2}\text{ [subtract and expand factorial and divide out common factors]}\\ P{}_3=60\text{ [multiply]}\end{array}$

Hence,The number of permutations for $P{}_3$ is $60$ .