Chapter 11.6, Problem 5C

To determine

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

Answer to Problem 5C

The number of permutations for $P{}_2$ is $30$ .

Explanation of Solution

Given : the expression is $P{}_2$ .

Formula used:

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

Calculation : tofind the number of permutations , put $n=6$ and $r=2$ , then simplify the result.

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

  $\begin{array}{l}P{}_2=\frac{6!}{\left(6-2\right)!}\text{ [substitue the n by 6 and r by 2]}\\ P{}_2=\frac{6·5·4·3·2·1}{4·3·2·1}\text{ [subtract, expand factorial, divide out common factors]}\\ P{}_2=30\text{ [multiply]}\end{array}$

Hence,The number of permutations for $P{}_2$ is $30$ .