This problem confused me.
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?
Thanks in advance!
The best way to see this is to take a "reverse" approach
The total number of possible teams is C(14, 6) = 3003 teams
Now assume that the triplets are all on one team....and for the remaining players, we can choose any 3 of the remaining 11...so this gives C(11,3) = 165 teams
So...the total number of teams that don't include all three triplets is
3003 - 165 =