swerve wrote:At a dinners party, 5 people are seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

A. 5
B. 10
C. 24
D. 32
E. 120

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

You can start by calculating the number of permutations of 5 people. For example, pick a chair to begin with. There are 5 ways to fill that chair. Continue clockwise with the remaining people, so :

5x4x3x2x1 = 120 arrangements

However, visualize that contributing to the total number of arrangements are arrangements where the same relative positioning of the five people is maintained but that each person is shifted one chair clockwise. Since question asks for those arrangements where only the relative positions are different, you need to divide 120 by 5 = 24,C