At least two women — Aptitude Question
At least two women: From 4 men and 3 women, in how many ways can a committee of 3 be formed with at least 2 women? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
From 4 men and 3 women, in how many ways can a committee of 3 be formed with at least 2 women?
Options
- 12
- 13
- 18
- 22
Show the answer and the worked solution
Correct answer: B. 13
Worked solution
- Exactly 2 women: C(3,2) × C(4,1) = 3 × 4 = 12.
- Exactly 3 women: C(3,3) = 1.
- Total = 12 + 1 = 13.
Answer: 13.
The idea
'At least k' means adding the separate cases. Here the complement route is no shorter, so enumerate the two cases directly.
Shortcut. Cross-check from the other side: C(7,3) = 35 committees in all, 4 with no woman and 3 × 6 = 18 with one, so 35 − 22 = 13.
Common trap. "12" — counting only committees with exactly 2 women (3 × 4) and forgetting the all-women committee that 'at least 2' also includes.
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