Question

In how many ways can the committee of 4 women and 2 men can be selected from a group of 10 women and 5 men If there are no restriction?

Answer 1

$$C(10, 4)C(5, 2)=\dbinom{10}{4}\dbinom{5}{2}$$

$$=\dfrac{10!}{4!(10-4)!}\cdot\dfrac{5!}{2!(5-2)!}=210\cdot10$$

$$=2100$$

The committee of 4 women and 2 men can be selected from a group of 10 women and 5 men If there are no restriction, in 2100 ways.