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2008/09 AHSMC Part 1 Problem 12

Problem 12 of 16

Of the eight members of a Sports Club, two are senior boys, two are senior girls, two are junior girls and two are junior boys. An official team is of size four, and must consist of two seniors and two juniors, as well as two girls and two boys. The number of different official teams is

Answer choices

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Solution

If we take both senior boys, we must complement them with both junior girls. If we take neither senior boy, we must take both senior girls and both junior boys. If we take only one senior boy, then we must take one senior girl, one junior girl and one junior boy. In each category, there are two choices. Hence the number of different teams is 1+1+24=181 + 1 + 2^4 = 18. The answer is (E).

University of Alberta