Question
Consider the following for the two (02) items that follow: A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies. What is the probability that the committee includes exactly 3 gentlemen?
NDA
Mathematics
Probability
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 10 33
- B. 30 77
- C. 100 231
- D. 5 11
Answer
A. 10 33
Step-by-step solution
Total number of people = 7 + 4 = 11 Total number of ways to select a committee of 6 members = ^ 11 C_ 6 To form a committee of 6 members with exactly 3 gentlemen, the remaining 3 members must be ladies. Number of ways to select exactly 3 gentlemen and 3 ladies = ^ 7 C_ 3 ^ 4 C_ 3 Required probability = ^ 7 C_ 3 ^ 4 C_ 3 ^ 11 C_ 6 ^ 11 C_ 6 = 11 10 9 8 7 6 6 5 4 3 2 1 = 462 ^ 7 C_ 3 = 7 6 5 3 2 1 = 35 ^ 4 C_ 3 = 4 Required probability = 35 4 462 = 140 462 = 10 33 Answer: 10 33
Related: Mathematics — Probability · All PYQ Banks