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 at least 2 ladies?
NDA
Mathematics
Probability
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 41 66
- B. 47 66
- C. 49 66
- D. 53 66
Answer
D. 53 66
Step-by-step solution
Total number of people is 7 + 4 = 11. Total number of ways to select a committee of 6 members is ^ 11 C_ 6 = 462. The number of ways to form a committee with less than 2 ladies (i.e., 0 or 1 lady) is ^ 4 C_ 0 ^ 7 C_ 6 + ^ 4 C_ 1 ^ 7 C_ 5 . ^ 4 C_ 0 ^ 7 C_ 6 = 1 7 = 7 ^ 4 C_ 1 ^ 7 C_ 5 = 4 21 = 84 Total number of ways with less than 2 ladies is 7 + 84 = 91. Number of ways to form a committee with at least 2 ladies is 462 - 91 = 371. Required probability is 371 462 = 53 66 . Answer: 53 66
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