A 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?
Here's what I think
Total possible teams = C(14, 6) = 3003 teams
Total teams that include all three triplets = choose the three triplets and then, from the remaining 11 people, choose any 3 of them = C(11,3) = 165 teams
Total teams that don't include the three triplets = 3003 - 165 = 2838 teams