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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!

 Feb 22, 2019

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



cool cool cool

 Feb 22, 2019
edited by CPhill  Feb 22, 2019


KingJom  Feb 23, 2019

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