Chapter 6, Problem 35CR

To determine

To find:the possible outfits from $6shirts$ and $3pants$ .

Answer to Problem 35CR

The possible outfits from $6shirts$ and $3pants$ is $18$ .

Explanation of Solution

Given information :

  $6shirts$ and $3pants$ .

Formula used:

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

Calculation : to findthe possible outfits , it is needed to choose 1 shirt from $6shirts$ and 1 pant from $3pants$ so from using combination find the possible outfits,

  $\begin{array}{l}C{}_1=\frac{6!}{1!\left(6-1\right)!}\text{ [substitute n by 6 and r by 1]}\\ C{}_1=\frac{6·5!}{1!\left(5\right)!}\text{ [subtract, expand factorial and divide out common factors]}\\ C{}_1=6\text{ [simplify]}\end{array}$

  $\begin{array}{l}C{}_1=\frac{3!}{1!\left(3-1\right)!}\text{ [substitute n by 3 and r by 1]}\\ C{}_1=\frac{3·2!}{1!\left(2\right)!}\text{ [subtract, expand factorial and divide out common factors]}\\ C{}_1=3\text{ [simplify]}\end{array}$

The multiply the both results because there is 3 possibilities with 1 shirt,

Total possible outfits = $\begin{array}{l}6·3\\ 18\end{array}$ [multiply]

Hence,The possible outfits from $6shirts$ and $3pants$ is $18$ .