Chapter 11.6, Problem 25E

To determine

To calculate:the number of permutations for $P{}_6$ .

Answer to Problem 25E

The number of permutations for $P{}_6$ is $13366080$ .

Explanation of Solution

Given : the expressionis $P{}_6$ .

Formula used:

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

Calculation : tofind the number of permutations , put $n=18$ and $r=6$ , then simplify the result.

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

  $\begin{array}{l}P{}_6=\frac{18!}{\left(18-6\right)!}\text{ [substitue n by 18 and r by 6]}\\ P{}_6=\frac{18·17·16·15·14·13·12!}{12!}\text{ [subtract, expand factorial and divide out common factors]}\\ P{}_6=13366080\text{ [multiply]}\end{array}$

Hence,The number of permutations for $P{}_6$ is $13366080$ .