A team with a captain — Aptitude Question
A team with a captain: From 8 players, in how many ways can a team of 3 be chosen and one of them named captain? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
From 8 players, in how many ways can a team of 3 be chosen and one of them named captain?
Options
- 56
- 112
- 168
- 336
Show the answer and the worked solution
Correct answer: C. 168
Worked solution
- Choose 3 from 8: C(8,3) = 56.
- Choose the captain from those 3: 3 ways.
- Total = 56 × 3 = 168.
Answer: 168.
The idea
Break a two-stage choice into stages and multiply. Choosing the captain first from all 8 and then two others gives 8 × C(7,2) = 168 as well.
Shortcut. Half of P(8,3) = 336 also works: an ordered triple with the captain first counts each team twice, once per order of the other two — 336 ÷ 2 = 168.
Common trap. "56" — counting the C(8,3) teams and forgetting that each team can name any of its 3 members as captain.
All Permutations & Combinations questions · placement mock tests