Our school's girls volleyball team has 14 players, including a set of 3 triplets: Missy, Lauren, and Liz. In how many ways can we choose 5 starters if the only restriction is that not all 3 triplets can be in the starting lineup?
If no triplets are on the team = C(11,5) = 462 possible teams
If one triplet is on the team C (3,1) * C( 11,4) = 990 possible teams
If two triplets are on the team = C(3,2) * C ( 11, 3) = 495 possible teams
So 462 + 990 + 495 =
1947 different teams
