Six people around a round table — Aptitude Question
Six people around a round table: In how many ways can 6 people be seated around a round table? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
In how many ways can 6 people be seated around a round table?
Options
- 60
- 120
- 240
- 720
Show the answer and the worked solution
Correct answer: B. 120
Worked solution
- Fix one person to remove rotations; the remaining 5 can be arranged in 5! ways.
- 5! = 120.
Answer: 120.
The idea
Circular arrangements of n people = (n − 1)!. If the table can also be flipped (necklaces, garlands), halve it again: (n − 1)!/2.
Shortcut. The 6! = 720 straight-line seatings count each round seating 6 times, once per rotation, so 720 ÷ 6 = 120.
Common trap. 720 — 6!, treating the round table as a row; rotating everyone one seat gives the same seating.
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