CA Foundation · Quantitative Aptitude · Permutations and Combinations
Six directors of a company in Pune are to be seated around a circular table for a board meeting. In how many distinct ways can they be seated if only their positions relative to one another matter?
The number of ways is 120. In a circular arrangement of 6 distinct people, rotating everyone by one seat gives the same relative order, so one person's position is fixed and the other five are arranged in 5! = 120 ways. Using 6! would count rotations as separate arrangements.
- A720
- B24
- C120Correct
- D60
Explanation
For n distinct persons around a circle, rotations are treated as the same arrangement, so the count is (n-1)!. Here it is 5! = 120. The figure 720 (6!) is wrong because it counts rotations of the same seating as different.
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