Chapter 11.6, Problem 27E

To determine

To calculate: the different possible arrangements of shirts for 5 days.

Answer to Problem 27E

the different possible arrangements of shirts for 5 days is $6720$ .

Explanation of Solution

Given :

Total shirts = $8$

Taken shirts = $5$

Formula used:

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

Calculation : tofind thedifferent possible arrangements of shirts for we have to choose 5 shirts among 8, so put the value in the above formula.

  $\begin{array}{l}P{}_5=\frac{8!}{\left(8-5\right)!}\text{ [substitue n by 8 and r by 5]}\\ P{}_5=\frac{8!}{3!}\text{ [subtract, expand factorial and divide out common factors}]\\ P{}_5=8·7·6·5·4\\ P{}_5=6720\text{ [multiply]}\end{array}$

Hence,the different possible arrangements of shirts for 5 days $6720$ .