Loyalist CVI is about to have a reunion of all the previous graduating classes. There are 20 members of the current alumni association. Of these, eight members are recent graduates. In how many ways can a sub-committee of four members be struck to provide memorabilia if

a) there are no restrictions
b) the sub-committee must be all recent graduates
c) the sub-committee must have only two recent graduates
d) the sub-committee must have no more than three graduates

I have trouble answering this could you please explain how you got it. Thanks!

Loyalist CVI is about to have a reunion of all the previous graduating classes. There are 20 members of the current alumni association. Of these, eight members are recent graduates. In how many ways can a sub-committee of four members be struck to provide memorabilia if


a) there are no restrictions

Here we just choose 4 from 20.


b) the sub-committee must be all recent graduates

We have to choose the 4 from the 8 recent grads and 0 from the remaining 12 non-recent grads: C(8,4)C(12,0)


c) the sub-committee must have only two recent graduates

Choose two from the recent grad and 2 from the other 12 non-recent grads:

C(8,2)C(12,2)


d) the sub-committee must have no more than three graduates

See if you can get this one.