. The number of ways in which a committee of 3 ladies and 4 gentlemen can

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