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 α 1 be the total number of ways in which the committee can be formed such…

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

α_{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

α_{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

α_{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

α_{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
A. The value of $α_{1}$ is	P. $136$
B. The value of $α_{2}$ is	Q. $189$
C. The value of $α_{3}$ is	R. $192$
D. The value of $α_{4}$ is	S. $200$
	T. $381$
	U. $461$

The correct option is:

Aicharya · Accepted Answer

1 α 1 = 6 3 5 2 = 200 So P → 4 2 α 2 = 6 1 5 1 + 6 2 5 2 + 6 3 2 3 + 6 4 5 4 + 6 5 5 5 = 11 5 - 1 = 461 So Q → 6 3 α 3 = 5 2 6 3 + 5 3 6 2 + 5 4 6 1 + 5 5 6 0 = 11 5 - 5 0 6 5 - 5 1 6 4 = 381 So R → 5 4 α 2 = 5 2 6 2 - 4 1 5 1 + 5 3 6 1 - 4 2 1 1 + 5 4 = 189 So S → 2

In a high school, a committee has to be formed from a group of 6 boys M 1 ,   M 2 ,   M 3 ,  …

Solution

In a high school, a committee has to be formed from a group of 6 boys M 1 , &#160; M 2 , &#160; M 3 , &#160;…

Solution

In a high school, a committee has to be formed from a group of 6 boys M 1 , M 2 , M 3 , …