Question

A committee of 8 persons is to be constituted from a group of 5 women and 7 men. In how many ways can this be done? In how many ways can the committee be formed if it consists of atleast 3 women and 3 men? What value is depicted by taking men and women in forming the committee?

Answer 1

$\to$ Total condidates $=5+7=12$

$8$ people can be selected out of $12$ people in $C(12,8)$

$=\frac{12!}{4!8!}=\frac{12\times 11\times 10\times 9}{4\times 3\times 2\times 1}$

$=495$ ways

committee with $3$ women and $3$ man atleasr

${}^5{C}_3{.}^7{C}_3=\frac{5!}{3!2!}.\frac{7!}{3!4!}$

$=\frac{5\times 4\times 3}{3\times 2}.\frac{7\times 5\times 5\times 4!}{3\times 4!\times 2}$

$=10.35$

$=350$ ways

The value depicted by taking man and woman is $350$