CA Foundation · Quantitative Aptitude · Permutations and Combinations
In how many different ways can 7 friends be seated around a circular table if only the relative positions of the friends matter (rotations are treated as the same arrangement)?
The number of circular arrangements of 7 distinct persons is (7-1)! = 720. One person's position fixes the reference point, and the remaining 6 can be arranged in 6! ways. Using 7! = 5040 would wrongly count rotations of the same seating as different.
- A5040
- B720Correct
- C840
- D360
Explanation
For n distinct persons around a circular table the number of arrangements is (n-1)!. Here it is (7-1)! = 6! = 720. The value 5040 is 7!, which wrongly treats rotations as different arrangements.
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