Since the committee of 5 is to be formed from 6 gents and 4 ladies.

(i) Forming a committee with at least 2 ladies

Here the possibilities are

(i) 2 ladies and 3 gents

(ii) 3 ladies and 2 gents

(iii) 4 ladies and 1 gent

the number of ways they can be selected

= ⁴C₂ ⁶C₃ + ⁴C₃ ⁶C₂ + ⁴C₄ ⁶C₁

Applying ⁿC_r =

= 186 ways

(ii) The number of ways in this case is

1. 0 ladies and 5 gents

2. 1 lady and 4 gents

3. 2 ladies and 3 gents.

The total ways are

= ⁴C₀ ⁶C₅ + ⁴C₁ ⁶C₄ + ⁴C₂ ⁶C₃

Applying ⁿC_r =

= 186 ways.