Question

How many different committees of 3 people can be chosen to work on a special projectfrom a group of 9 people?

Answer 1

If the group has 9 people and we want to calculate how many subgroups of 3 people can be done, we have a combination of 9 choose 3.

A combination of n choose p can be calculated with the formula below:

$C(n,p)=\frac{n!}{p!(n-p)!}$

So, for n = 9 and p = 3, we have:

$C(9,3)=\frac{9!}{3!(9-3)!}=\frac{9\cdot8\cdot7\cdot6!}{3\cdot2\cdot6!}=84$

Therefore 84 different committees can be made.