A committee of three — Aptitude Question
A committee of three: In how many ways can a committee of 3 people be chosen from 5 men and 4 women so that it has… Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
In how many ways can a committee of 3 people be chosen from 5 men and 4 women so that it has exactly 2 men?
Options
- 30
- 40
- 60
- 84
Show the answer and the worked solution
Correct answer: B. 40
Worked solution
- Ways to choose 2 men from 5 = C(5,2) = 10.
- Ways to choose 1 woman from 4 = C(4,1) = 4.
- Total = 10 × 4 = 40.
Answer: 40.
The idea
Independent choices multiply. Selection uses combinations because the order within a committee does not matter.
Shortcut. C(5,2) is the handshake count for 5 people, 10, and exactly two men leaves one seat for any of the 4 women: 10 × 4 = 40.
Common trap. "84" — computing C(9,3), every committee of 3 from the 9 people, and dropping the 'exactly 2 men' condition.
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