UPSC NDA I 2025 Mathematics Paper

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

11

6

)=‌

11×10×9×8×7×6

6×5×4×3×2×1

=462
The number of ways to form a committee with exactly 3 gentlemen and 3 ladies is:
(

7

3

)×(

4

3

)=35×4=140
The probability of forming a committee with exactly 3 gentlemen is:
Probability =‌

140

462

=‌

10

33