SOLUTION: 5 stdnts to be chosen in a chess club from 6 boys and 8 girls. How many ways it is possible to form the comittee if 3 of the boys are cousins and are either all in the team or none

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Question 935921: 5 stdnts to be chosen in a chess club from 6 boys and 8 girls. How many ways it is possible to form the comittee if 3 of the boys are cousins and are either all in the team or none?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
5 students to be chosen in a chess club from 6 boys and 8 girls. How many ways is
it possible to form the comittee if 3 of the boys are cousins and are either all
in the team or none are?
Case 1:  We choose all 3 cousins.

Then we have the other 3 boys remaining and 8 girls. That's 11 people, but we
have only 2 more to choose, so that's C(11,2) ways.

Case 2:  We do not choose any of the three cousins.  As before we have the other
3 boys and the 8 girls to choose from.  That's 11 people, but this time we must
choose all 5 from the 11, so that's C(11,5) ways.

Answer C(11,2)+C(11,5) = 55+462=517 ways.

Edwin
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