2015/16 AHSMC Part 1 Problem 8

Problem 8 of 16

There are $5$ boys and $6$ girls in a class. A committee of three students is to be made such that there is a boy and a girl on the committee. In how many different ways can the committee be selected?

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Solution

The number of committees of $3$ students made with $11$ students is $\dbinom{11}{3} = 165$ . The number of committees of three girls or three boys is $\dbinom{6}{3} + \dbinom{5}{3} = 20 + 10 = 30$ . The number of requested committees is $165-30=135$ . The answer is (B).

University of Alberta

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