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