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 6 starters if the only restriction is that not all 3 triplets can be in the starting lineup?
The total number of possible teams is
C(14,6) = 3003
Let all three triplets be on one team......
So the number of possible teams in this scenario is C(14,3) = 364
So....the number of teams that DON'T include all three of the triplets is
3003 - 364 = 2639