. 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

B: 1540

C: 3240

D: none of these

 

Best Answer

Explanation:

3 ladies out of 8 can be selected in C38 ways and 4 gentlemen out of 7 in C47  ways.

Now each way of selecting 3 ladies is associated with each way of selecting 4 gentlemen.

So, the required number of ways = C38×C47= 56×35=1960.

We can now find the number of committees of 3 ladies and 4 gentlemen in which both Mrs X and Mr Y are members.

In this case we can select 2 other ladies from the remaining 7 in C27ways and 3 other gentlemen from the remaining 6 in C36ways.

Therefore the number of ways in which both Mrs X and Mr Y are always included C27×C38=21×20=420.

Hence the required number of committee in which Mrs X and Mr Y do not serve together =1960-420=1540. 

Final answer:

The number of ways is 1540, (B) option is correct

 

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