Question

Forming a Committee A student dance committee is to be formed consisting of 2 boys and 3 girls. If the membership is to be chosen from 4 boys and 8 girls, how many different committees are possible?

Short answer

There are 336 ways to form a committee.

Step-by-step solution

Step 1. Given information.

The number of boys is 4.

The number of girls is 8.

We need to form a committee of 2 boys and 3 girls.

Step 2. Determine the number of possible committees.

The order of being selected for a committee is not significant. So, the problem asks for the number of combinations of 4 boys taken 2 at a time and the number of combinations of 8 girls taken 3 at a time.

$\begin{array}{rcl}C(4,2)·C(8,3)& =& \frac{4!}{(4-2)!2!}·\frac{8!}{(8-3)!3!}\\ & =& \frac{4!}{2!2!}·\frac{8!}{5!3!}\\ & =& \frac{4·3·2!}{2·1·2!}·\frac{8·7·6·5!}{5!·3·2·1}\\ & =& 336\end{array}$

Step 3. Conclusion.

There are 336 ways to form a committee.