Q.)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

(a) 1960

(b) 3240

(c) 1540

(d) None of these

[SNAP 2013 Question , SNAP Questions , Permutations and Combinations]

Solution :

Case I : When Mr. Y is included in the committee :

Then , we need to select 3 ladies from 7 ladies and 3 gentlemen from 6 gentlemen as Y is included and Mrs. X refuses to be in committee.

No of ways =

=

= 35*20 = 700

Case II : When Mr. Y is not included in the committee :

Then , we need to select 3 ladies from 8 ladies and 4 gentlemen from 6 gentlemen as Y is not included.

No of ways =

= 56 * 15 = 840

Hence, total number of ways = 700 + 840 = 1540

Hence , OPTION(c)