In how many different ways can it be done so that the committee has at least one woman?

Explanation:

The committee of 4 persons is to be so formed that it has at least 1 woman.

The different ways that we can choose to form such a committee are:

(i) 1w. 3 m in 4C1×6C3

= 4× 6×5×4\3×2×1 = 80

(ii) 2w. 2m in 4C2×6C2

= 4×3\ 2×1 × 6×5\ 2×1 = 90

(iii) 3w. 1m in 4C3×6C1

= 4×6 = 24

(iv) 4w in 4C4 = 1

Therefore, Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman

= 80 + 90 + 24 + 1 = 195