A property of combinations — Aptitude Question
A property of combinations: What is the value of C(12, 10)? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
What is the value of C(12, 10)?
Options
- 22
- 66
- 132
- 220
Show the answer and the worked solution
Correct answer: B. 66
Worked solution
- C(12,10) = C(12,2) = (12 × 11)/2 = 66.
Answer: 66.
The idea
Use the symmetry C(n,r) = C(n, n−r) to replace a large r with a small one. It turns a long calculation into a short one.
Shortcut. Choosing the 10 to include is the same as choosing the 2 to leave out, so this is a handshake count: 12 × 11 ÷ 2 = 66.
Common trap. "132" — computing 12 × 11 and forgetting to divide by 2!, the order of the two left out.
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