Question

In a high school, a committee has to be formed from a group of 6 boys $M_{1}, M_{2}, M_{3}, M_{4}, M_{5}, M_{6}$ and 5 girls $G_{1}, G_{2}, G_{3}, G_{4}, G_{5}$.
(i) Let $\alpha_{1}$ be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls.
(ii) Let $\alpha_{2}$ be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls.
(iii) Let $\alpha_{3}$ be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls.
(iv) Let $\alpha_{4}$ be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls and such that both $M_{1}$ and $G_{1}$ are NOT in the committee together.

| LIST-I | | LIST-II | |
| --- | --- | --- | --- |
| P. | The value of $\alpha_{1}$ is | 1. | 136 |
| Q. | The value of $\alpha_{2}$ is | 2. | 189 |
| R. | The value of $\alpha_{3}$ is | 3. | 192 |
| S. | The value of $\alpha_{4}$ is | 4. | 200 |
| | | 5. | 381 |
| | | 6. | 461 |

The correct option is:

Accepted Answer

(C) $\mathbf{P} \rightarrow 4 ; \mathbf{Q} \rightarrow \mathbf{6} ; \mathbf{R} \rightarrow \mathbf{5} ; \mathbf{S} \rightarrow \mathbf{2}$

Answer

(A) $\mathbf{P} \rightarrow 4 ; \mathbf{Q} \rightarrow 6 ; \mathbf{R} \rightarrow 2 ; \mathbf{S} \rightarrow \mathbf{1}$

Answer

(B) $\mathbf{P} \rightarrow 1 ; \mathbf{Q} \rightarrow 4 ; \mathbf{R} \rightarrow 2 ; \mathbf{S} \rightarrow 3$

Answer

(D) $\mathbf{P} \rightarrow 4 ; \mathbf{Q} \rightarrow 2 ; \mathbf{R} \rightarrow \mathbf{3} ; \mathbf{S} \rightarrow \mathbf{1}$

JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Permutations and Combinations

Solution

More JEE Advanced questions on Permutations and Combinations

LIST-I		LIST-II
P.	The value of $α_{1}$ is	1.	136
Q.	The value of $α_{2}$ is	2.	189
R.	The value of $α_{3}$ is	3.	192
S.	The value of $α_{4}$ is	4.	200
		5.	381
		6.	461