Question

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. If how many ways can this be done ?

How many of these committees would consists of 1 man and 2 women ?

Answer 1

The number of ways selecting of 3 people out of 5

${=}^5{C}_3=\frac{5!}{3!2!}=\frac{5\times 4}{2}=10$

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

${=}^2{C}_1{\times }^3{C}_2$

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

$=6$