A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?

Question

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women? (A) 10, 4 (B) 10, 6 (C) 5, 4 (D) 6, 4

Tardigrade Admin · Accepted Answer

There will be as many committees as there are combinations of

5

different persons taken

3

at a time. Hence, the required number of ways

=^{5} C_{3} = \frac{5 !}{3 ! 2 !}

= \frac{4 \times 5}{2} = 10

.
Now,

1

man can be selected from

2

men in

^{2} C_{1}

ways and

2

women can be selected from

3

women in

^{3} C_{2}

ways. Therefore, the required number of committees

=^{2} C_{1} \times^{3} C_{2}

= \frac{2 !}{1 ! 1 !} \times \frac{3 !}{2 ! 1 !} = 6

Q. A committee of $3$ persons is to be constituted from a group of $2$ men and $3$ women. In how many ways can this be done? How many of these committees would consist of $1$ man and $2$ women?

$10, 4$

$10, 6$

$5, 4$

$6, 4$

Q. A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?

10,4

10,6

5,4

6,4

Q. A committee of $3$ persons is to be constituted from a group of $2$ men and $3$ women. In how many ways can this be done? How many of these committees would consist of $1$ man and $2$ women?

$10, 4$

$10, 6$

$5, 4$

$6, 4$