Chapter 11.6, Problem 6E

To determine

To calculate: the number of permutations for $P{}_0$ .

Answer to Problem 6E

The number of permutations for $P{}_0$ is $1$ .

Explanation of Solution

Given : the expressionis $P{}_0$ .

Formula used:

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

Calculation : tofind the number of permutations , put $n=6$ and $r=0$ , then simplify the result.

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

  $\begin{array}{l}P{}_0=\frac{6!}{\left(6-0\right)!}\text{ [substiute n by 6 and r by 0]}\\ P{}_0=\frac{6·5·4·3·2·1}{6!}\text{ [subtract, expand factorial]}\\ P{}_0=1\text{ [divide out the common factors]}\end{array}$

Hence,The number of permutations for $P{}_0$ is $1$ .