Chapter 11.6, Problem 5E

To determine

To calculate: the number of permutations for $P{}_2$ .

Answer to Problem 5E

The number of permutations for $P{}_2$ is $2$ .

Explanation of Solution

Given : the expressionis $P{}_2$ .

Formula used:

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

Calculation : tofind the number of permutations , put $n=2$ and $r=2$ , then simplify the result.

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

  $\begin{array}{l}P{}_2=\frac{2!}{\left(2-2\right)!}\text{ [substitue n by 2 and r by 2]}\\ P{}_2=\frac{2·1}{0!}\text{ [subtract, expand factorial]}\\ P{}_2=\frac{2}{1}\text{ [0!=1]}\\ P{}_2=2\text{ [divide]}\end{array}$

Hence,The number of permutations for $P{}_2$ is $2$ .