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 its member, is

Here we have two cases:

Case 1: If Y is a member of the committee

We have to select 3 other gentlemen and 3 ladies from 8 ladies and 5 gentlemen (Since If Y is a member of the committee, X will not be a member of the committee)

=$$^7C_3\times\ ^6C_3$$ =35*20=700.

Case 2: If Y is not a member of the committee

We have to select 4 gentlemen and 3 ladies from 8 ladies and 6 gentlemen (Since Y is not a member of the committee)

=$$^8C_3\times\ ^6C_4$$ = 56*15=840

Total cases = 700+840 = 1540

C is the correct answer.