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:

• A. P $\to$ 4; Q $\to$ 6; R $\to$ 2; S $\to$ 1
• B. P $\to$ 1; Q $\to$ 4; R $\to$ 2; S $\to$ 3
• C. P $\to$ 4; Q $\to$ 6; R $\to$ 5; S $\to$ 2
• D. P $\to$ 4; Q $\to$ 2; R $\to$ 3; S $\to$ 1

Answer 1

Answer: (C)

Correct answer is (c) P $\to$ 4; Q $\to$ 6; R $\to$ 5; S $\to$ 2