Question

From a group of 7 women and 5 men, a committee consisting of 4 women and 3 menis to be formed. How many different committees are possible if
a) there are no restrictions?
b) 2 of the women refuse to serve together?

Answer 1

Answer:

(a) Number of  committees formed if there are no restrictions = 350

(b) Number of  committees formed if 2 of the women refuse to serve together = 310

Step-by-step explanation:

As per the question,

Number of women = 7

Number of men = 5

The different committees are possible if

(a) There are no restrictions

Number of  committees formed

= $^{7}C_{4} \times ^{5}C_{3}$

= 350

(b) 2 of the women refuse to serve together

From the 350, we must subtract the number of ways those two women serve together.

If the men and women both serve together, then 1 woman serve with 4 men.

The men are chosen

$=^{5}C_{3} = 10\ ways$,

So

The number we must subtract from the 350 is  4 × 10 = 40

∴ Number of  committees formed  = 350 - 40 = 310.