Out of 5 men and 2 women, a committee of 3 is to be formed. In how man

1.	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» (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.

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»

(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.