Arithmetic Ability
Permutations and Combinations

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Q.

From a total of six men and four ladies a committee of three is to be formed. If Mrs. X is not willing to join the committee in which Mr. Y is a member, whereas Mr.Y is willing to join the committee only if Mrs Z is included, how many such committee are possible?

View Answer

Correct choice: A

Explanation:

We first count the number of committee in which (i). Mr. Y is a member (ii). the ones in which he is not Case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member. Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join). We can choose 1 more in5+2C1=7 ways. Case (ii): If Mr. Y is not a member then we left with (6+4-1) people. we can select 3 from 9 in 9C3=84 ways. Thus, total number of ways is 7+84= 91 ways.
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