Question

Out of 5 men and 2 women, a committee of 3 is to be formed. In how many ways can it be formed if at least one woman is to be included?

(a) 15 

(b) 25 

(c) 20 

(d) 10

Answer 1

(b) 25 

If at least one woman has to be included then the committee can be formed as: 

• 1 woman and 2 men 

• 2 women and 1 man 

∴ Number of ways of forming the committee 

= ²C₁ × ⁵C₂ + ²C₂ × ⁵C₁ 

= 2 × 10 + 1 × 5 = 20 + 5 = 25.