Assume that the committee consists of 10 Republicans and 4 Democrats. A subcommittee consisting of 6 people is to be selected.

Question

(1) How many such subcommittees are possible if each subcommittee must contain exactly 4 Republicans and 2 Democrats? 

(1) How many such subcommittees are possible if each subcommittee must contain at least 1 and no more than 2 Democrats? 

Answer 1

1) (10 choose 4)(4 choose 2)

2) (10 choose 5)(4 choose 1) + (10 choose 4)(4 choose 2)

Use answer from part 1