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!

KingJom Feb 22, 2019

#1**+3 **

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 =

2838 teams

CPhill Feb 22, 2019