As they mentioned there will be 2 ladies in a committee of 5 members. There is 6-gents 4-ladies
Case-1-2 ladies- 4c2×6c3=120
case-2-3 ladies- 4c3×6c2=60
case-3-4 ladies-4c4×6c1=6
》No.of combinations of 5 committee members formed by 4 ladies and 6 gents =120+60+6=186

There are 6 gents and 4 ladies, and a committee of 5 members needs to be formed such that it includes at least 2 ladies. Let's analyze the possible scenarios and explain in detail how to form such a committee.

Scenario 1: Selecting 2 ladies and 3 gents
In this scenario, we will select 2 ladies from the 4 available, and the remaining 3 members will be selected from the 6 gents.

- Number of ways to select 2 ladies from 4: C(4, 2) = 6 (where C(n, r) represents the combination of selecting r elements from a set of n elements)
- Number of ways to select 3 gents from 6: C(6, 3) = 20

Using the multiplication principle, the total number of possible committees in this scenario is 6 * 20 = 120.

Scenario 2: Selecting 3 ladies and 2 gents
In this scenario, we will select 3 ladies from the 4 available, and the remaining 2 members will be selected from the 6 gents.

- Number of ways to select 3 ladies from 4: C(4, 3) = 4
- Number of ways to select 2 gents from 6: C(6, 2) = 15

Using the multiplication principle, the total number of possible committees in this scenario is 4 * 15 = 60.

Total number of committees with at least 2 ladies
To find the total number of committees, we need to sum up the number of committees from both scenarios.

Total number of committees = 120 + 60 = 180

Therefore, there are 180 possible committees that can be formed with at least 2 ladies from a group of 6 gents and 4 ladies.