Choosing a team — Aptitude Question
Choosing a team: In how many ways can a team of 4 be chosen from 9 players? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 60 seconds
Question
In how many ways can a team of 4 be chosen from 9 players?
Options
- 84
- 126
- 252
- 3,024
Show the answer and the worked solution
Correct answer: B. 126
Worked solution
- C(9,4) = 3,024 ÷ 24 = 126.
Answer: 126.
The idea
Selection uses combinations. The permutation P(9,4) = 3,024 is offered for anyone who forgets to divide by 4!.
Shortcut. 9 × 8 × 7 × 6 ÷ 24: cancel 8 × 6 against 24 to leave 9 × 7 × 2 = 126.
Common trap. "3,024" — multiplying 9 × 8 × 7 × 6 and stopping, which counts ordered line-ups; a team has no order, so divide by 4! = 24.
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