The number of ways of choosing a committee of two women and three men from five women and six men, if Mr. A refuses to serve on the committee if Mr. B is a member and Mr. B can only serve, if Miss C is the member of the committee is
A
60
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B
84
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C
124
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D
None of these
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Solution
The correct option is C124 Case I: Mr. 'B' is present ∵ Mr. 'B' is present then according to the given condition Mrs 'C' needs to be in the committee and Mr. A should not be in the committee ⇒ 'A' is excluded and 'C' included
Hence, the number of ways is 4C24C1=24.
Case II: Mr. 'B' is absent ∵ Mr. 'B' is absent then according to the given condition Mrs 'C' can be in committee or not and Mr. A can be in the committee or not ⇒ No constraint
Hence, the number of ways is 5C35C2=100 ∴ Total =124