Handshakes among twelve — Aptitude Question
Handshakes among twelve: If 12 people each shake hands with every other exactly once, how many handshakes occur? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
If 12 people each shake hands with every other exactly once, how many handshakes occur?
Options
- 60
- 66
- 72
- 132
Show the answer and the worked solution
Correct answer: B. 66
Worked solution
- C(12,2) = (12 × 11)/2 = 66.
Answer: 66.
The idea
Each handshake is a pair, so divide by 2. Forgetting to halve gives 132, which is offered.
Shortcut. The first person shakes 11 hands, the next 10 new ones, and so on: 11 + 10 + … + 1 = 66.
Common trap. "132" — counting 12 × 11 handshakes, which counts A-with-B and B-with-A as two.
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