Question

out of 5 men and 3 women a committee of 3 members is to be formed so that it has 1 woman and 2 men. in how many different ways can it be done

Answer 1

Final Answer : 30

Steps:
1) 3 members in which 1 women and 2 men
=> Select 1 women out of 3 and Select 2 men out of 5
$= > \binom{3}{1} \times \binom{5}{2} \\ = > 3 \times 10 = 30$

There are 30 Desired ways to do so.

Answer 2

We have to select 3 members such that 1 is woman and 3 are men

So,

1 woman can be selected from 3 women in

3C1 ways = 3 ways

And,

2 men can can be selected from 5 men in

5C2 ways = 10 ways

So,

Total number of combinations possible are,

=10 × 3

=30 ways