UPSC NDA I 2025 Mathematics Paper

Given,
A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies.
The total number of ways to form the committee is:
(

11

6

)=462
The favorable outcomes (at least 2 ladies) are calculated by the sum of the cases:
(

4

2

)×(

7

4

)+(

4

3

)×(

7

3

)+(

4

4

)×(

7

2

)
This simplifies to:
‌(

4

2

)×(

7

4

)=6×35=210
‌(

4

3

)×(

7

3

)=4×35=140
‌(

4

4

)×(

7

2

)=1×21=21
The total favorable outcomes are:
210+140+21=371
The probability is:
P(E)=‌

371

462

=‌

53

66