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
