A Senate committee has 8 Republicans and 6 Democrats. In how many ways can we form a subcommittee of 4 members that has at least one member from each party?
I think: 8 ways to pick a rep x 6 ways to pick a dem = 48 ways to get the requirement of one rep and one dem
then there are 12 to pick from for the other two memebers
12 c 2 = 66 ways
66 x 48 = 3168 ways