# 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?

A. 138

B. 128

C. 112

D. 91

**Answer: Option D **

__Solution(By Examveda Team)__

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 in

^{5+2}C

_{1}= 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

^{9}C

_{3}= 84 ways.

Thus, total number of ways is 7 + 84 = 91 ways.

### Click here to read 1000+ Related Questions on Permutation and Combination(Arithmetic Ability)

Related Questions on Permutation and Combination

A. 3! 4! 8! 4!

B. 3! 8!

C. 4! 4!

D. 8! 4! 4!

A. 7560,60,1680

B. 7890,120,650

C. 7650,200,4444

D. None of these

A. 8 × 9!

B. 8 × 8!

C. 7 × 9!

D. 9 × 8!

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