A club consists of 5 men and 5 women. A 5-member committee of 2 men and 3 women has to be constituted. Suppose Mrs. F refuses to work with Mr. M. How many ways are there of constituting a 5-member committee that ensures that the two of them do not work together?
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A club consists of 5 men and 5 women. A 5-member committee of 2 men and 3 women has to be constituted. Suppose Mrs. F refuses to work with Mr. M. How many ways are there of constituting a 5-member committee that ensures that the two of them do not work together? (A) 50 (B) 76 (C) 108 (D) None of the above
Combinatorics and counting has come up 24 times in 5 exams since 2009.
This question is on Inclusion-exclusion and complementary counting, part of Combinatorics and counting in Mathematics.
Counting by adding and removing overlaps, or by counting what is not wanted.
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Question from the DSE 2013 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.