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Question 50

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 of which Mr Y is its member, is

Solution

There are two conditions here,

(i) If Mr Y is in the committee then Mrs X will not be selected (or)

(ii) If Mr Y is not selected in the committee then Mrs X will be selected

$$\therefore$$ Total number of ways = $$8_{C_{3}} \times 6_{C_{4}} + 7_{C_{3}}\times 7_{C_{4}}$$

$$\Rightarrow$$ 56 x 15 + 35 x 35 = 2065

Hence, option D is the correct answer.

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