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A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then:

1. m + n = 68
2. m = n = 78
3. n = m - 8
4. m = n = 68

Correct answer: m = n = 78

Solution

At least 6 males (committee of 11): (6M,5F)=C(8,6)C(5,5)=28, (7M,4F)=C(8,7)C(5,4)=40, (8M,3F)=C(8,8)C(5,3)=10, so m=78. At least 3 females gives the same three cases, so n=78. Thus m = n = 78.

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