Eight people at a round table — Aptitude Question
Eight people at a round table: In how many ways can 8 people be seated around a circular table? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 50 seconds
Question
In how many ways can 8 people be seated around a circular table?
Options
- 720
- 5,040
- 40,320
- 362,880
Show the answer and the worked solution
Correct answer: B. 5,040
Worked solution
- Fix one person to remove rotations.
- The remaining 7 arrange in 7! = 5,040 ways.
Answer: 5,040.
The idea
Circular arrangements of n people = (n − 1)!. If the arrangement can also be flipped over, halve it again.
Shortcut. Divide the row count by the number of seats: 8! ÷ 8 = 40,320 ÷ 8 = 5,040, since each circular seating appears 8 times as a rotation.
Common trap. "40,320" — using 8! as for a row; around a table the 8 rotations of one seating are the same arrangement.
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