QR Question

[ZenoVT]

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Country A and Country B will form a joint committee on economic policy. The committee is to have exactly 6 members. 5 candidates for the committee come from Country A and 6 from Country B. If at least 3 members of the committee must come from Country A, how many distinct committees are possible?

 

[Streetwolf]

Country A and Country B will form a joint committee on economic policy. The committee is to have exactly 6 members. 5 candidates for the committee come from Country A and 6 from Country B. If at least 3 members of the committee must come from Country A, how many distinct committees are possible?

Well either 3, 4, or 5 would come from A. There need to be 6 members so that means either 3, 2, or 1 would come from B.

3/3 = (5c3) * (6c3) = 10 * 20 = 200
4/2 = (5c4) * (6c2) = 5 * 15 = 75
5/1 = (5c5) * (6c1) = 1 * 6 = 6

Total = 281