A two-member committee comprising of one male and one female member is to be constituted out of five males and three females. Amongst the females. Ms. A refuses to be a member of the committee in which Mr. B is taken as the member. In how many different ways can the committee be constituted?
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UPSC Civil Services preparation
- A11
- B12
- C13
- D14Correct
Explanation
To find the number of ways to form the committee, we first calculate the total possible combinations and then subtract the restricted case.
The committee must have one male and one female. There are 5 males and 3 females available. The total number of ways to form such a committee is 5 multiplied by 3, which equals 15.
However, there is one restriction: Ms. A and Mr. B cannot be in the same committee. There is only 1 specific committee where both are present (Mr. B and Ms. A).
To find the valid number of ways, subtract this 1 restricted case from the total combinations: 15 minus 1 equals 14.
Therefore, the committee can be constituted in 14 different ways. The correct option is D.

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