Chapter 11.6, Problem 42E

To determine

To explain: the expression $P{}_r=n!$ when $n=r$ .

Answer to Problem 42E

  $P{}_r=n!$

Explanation of Solution

Given : the expressionis $P{}_r=n!$ .

Formula used:

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

Calculation : toexplain it, put $n=r$ , then simplify the result, when we simplify it then denominator becomes $0!$ , and $0!=1$ .

  $\begin{array}{l}P{}_r=\frac{n!}{\left(n-r\right)!}\\ P{}_r=\frac{n!}{\left(r-r\right)!}\text{ [substitue n by r]}\\ P{}_r=\frac{n!}{0!}\text{ [subtract]}\\ P{}_r=n!\text{ [divide]}\end{array}$

Hence, $P{}_r=n!$ .