+0  
 
+3
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avatar+15 

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
 #1
avatar+98130 
+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

 

 

cool cool cool

 Feb 22, 2019
edited by CPhill  Feb 22, 2019
 #2
avatar+15 
+1

Thanks!

KingJom  Feb 23, 2019

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