Evaluating a combination — Aptitude Question
Evaluating a combination: What is the value of C(10, 3)? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
What is the value of C(10, 3)?
Options
- 30
- 72
- 120
- 720
Show the answer and the worked solution
Correct answer: C. 120
Worked solution
- C(10,3) = (10 × 9 × 8)/(3 × 2 × 1) = 720/6 = 120.
Answer: 120.
The idea
Write r factors from the top and r from the bottom. P(10,3) = 720 without the division, which is why 720 is offered.
Shortcut. Cancel before multiplying: 9 ÷ 3 = 3 and 8 ÷ 2 = 4, leaving 10 × 3 × 4 = 120.
Common trap. "720" — multiplying 10 × 9 × 8 and forgetting to divide by 3!; that is P(10,3), the ordered count.
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