Question

In how many ways a committee consisting of 3 men and 2 women can be chosen from 7 men and 5 women?
1. 45
2. 350
3. 4200
4. 230

Answer 1

Correct Answer - Option 2 : 350

Concept:

The number of ways to select r things out of n given things wherein r ≤ n is given by: \({\;^n}{C_r} = \frac{{n!}}{{r!\; \times \left( {n - r} \right)!}}\)

Calculation:

We have to select 3 men out of 7 men, so the number of ways of selection = ⁷C₃

Now, we have to select 3 women out of 5 women, so the number of ways of selection  = ⁵C₂

Required no. of ways = ⁷C₃ × ⁵C₂ = 350