Chapter 13.2, Problem 49AYU

To determine

To find: How many different committees are possible?

Answer to Problem 49AYU

336 different committees are possible.

Explanation of Solution

Given:

A student dance committee is to be formed consisting of 2 boys and 3 girls. The membership is to be chosen from 4 boys and 8 girls.

Formula used:

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

Calculation:

The committee of 2 boys and 3 girls is to be chosen from 4 boys and 8 girls.

Number of choices for boys is $C\left(4,2\right)=\frac{4!}{2!*2!}=6$.

Number of choices for girls is $C\left(8,3\right)=\frac{8!}{5!3!}=56$.

Hence, number of choices for forming a committee of 2 boys and 3 girls are $6*56=336$.