Selecting from two groups — Aptitude Question
Selecting from two groups: A committee of 5 is to be chosen from 6 men and 4 women so that it contains exactly 3… Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A committee of 5 is to be chosen from 6 men and 4 women so that it contains exactly 3 women. In how many ways?
Options
- 40
- 60
- 84
- 120
Show the answer and the worked solution
Correct answer: B. 60
Worked solution
- Women: C(4,3) = 4.
- Men: C(6,2) = 15.
- Total = 4 × 15 = 60.
Answer: 60.
The idea
Independent selections from separate groups multiply. Check the numbers add to the committee size: 3 + 2 = 5. ✓
Shortcut. Exactly 3 women forces exactly 2 men: C(4,3) = C(4,1) = 4 and C(6,2) = 15, so 4 × 15 = 60.
Common trap. "120" — choosing the 2 men as 6 × 5 = 30 without halving for order, then 4 × 30 = 120.
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