Question

From 9 names on a ballot, a committee of 5 will be elected to attend a political conference. How many different committees are possible?

Answer 1

Combinations are given by the expression:

$\begin{gathered} \text{nCr}=\frac{n!}{r!(n-r)!} \\ 9C_5=\frac{9!}{5!(9-5)!}=\frac{362880}{2880} \\ 9C_5=126 \end{gathered}$

There are 126 different comittees.