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Question

The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a meeting consisting of 8 ladies and 7 gentlemen, if Mrs X refuses to serve in a committee if Mr. Y is a member is

A
1960
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B
1540
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C
3240
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D
none of these
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Solution

The correct option is A 1540
3 ladies out of 8 can be selected in 8C3 ways and 4 gentlemen out of 7 in 7C4 ways.
Now each way of selecting 3 ladies is associated with each way of selecting 4 gentlemen.
Hence, the required number of ways =8C3×7C4=56×35=1960.
We now find the number of committee of 3 ladies and 4 gentlemen in which both Mrs X and Mr Y are member.
In this case we can select 2 other ladies from the remaining 7 in 7C2 ways and 3 other gentlemen from the remaining 6 in 6C3 ways.
The number of ways in which both Mrs X and Mr Y are always included =7C2×8C3=21×20=420
Hence the required number of committee in which Mrs X and Mr Y do not serve together =1960=420=1540.

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