Question

4 students from a class of 15 are going to be chosen to be on the dance committee. Findthe number of different 4-person committees that can be made.

Answer 1

`C(15,4)=1365\text{ different committees}`

Explanation:

This situation can be approached using the formula for combinations:

`\begin{gathered} C(n,r)=(n!)/(r!(n-r)!) \\ \text{where,} \\ n=\text{ number of possible items that can be }selected \\ r=\text{ number of items that were selected} \end{gathered}`

Therefore, solve for n=15 and r=4.

`\begin{gathered} C(15,4)=(15!)/(4!(15-4)!) \\ C(15,4)=1365\text{ different committees} \end{gathered}`