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# Pretty much stuck

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Rocco is a member of the Aviation Club, which has 12 members. The members need to choose a 3-person Helicopter Committee and a 4-person Glider Committee. A member can serve on one of the committees or both. Rocco refuses to serve on both (but he can serve on one of the committees). In how many ways can they form the committees?

Oct 13, 2019

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Rocco is a member of the Aviation Club, which has 12 members.

The members need to choose a 3-person Helicopter Committee and a 4-person Glider Committee.

A member can serve on one of the committees or both. Rocco refuses to serve on both (but he can serve on one of the committees).

In how many ways can they form the committees?

If rocco is on the helicopter committee then

there are   11C2*11C4 = 55*330 = 18150 ways

If rocco is on the Glider committee committee then

there are   11C3*11C3 = 165*165 = 27225 ways

If rocco is not on either committee then

there are   11C3*11C3 = 165*330 = 54450 ways

18150+27225+54450 = 99825 ways

Oct 13, 2019