Chapter 11.6, Problem 23E

To determine

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

Answer to Problem 23E

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

Explanation of Solution

Given : the expression is $P{}_0$ .

Formula used:

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

Calculation : tofind the number of permutations , put $n=11$ and $r=0$ , then simplify the result.

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

  $\begin{array}{l}P{}_0=\frac{11!}{\left(11-0\right)!}\text{ [substitute n by 11 and r by 0]}\\ P{}_0=\frac{11!}{11!}\text{ [subtract and divide out common factors]}\\ P{}_0=1\end{array}$

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