How many committees of five can be formed from a group of six Republicans and three Democrats if each committee is to have at least three Republicans?

Solution:

3 Republicans: N=C(6,3)*C(3,2)=20*3=60

4 Republicans: N=C(6,4)*C(3,1)=15*3=45

5 Republicans: N=C(6,5)*C(3,0)=6

So

60+45+6=111

So there are 111 committees