How would you do this one?

At a dinner party 5 people are to be seated arround a circular table. Tow seating arrangemets 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?

5,10,24,32,120

Answer is 24

Consider these as 5 seats around a round table.

5 people in a row will sit in 5*4*3*2*1 ways = 120 ways.

In circle, abcde = bcdea = cdeab = deabc = eabcd. So each different arrangement (by people's respective position) is actually reprsented 5 times in this 120. So divide by 5 and you get 24.

To add on to the point made by Guest - We can generalize this to any number of people. For any number N, the circular permutation formula is (N-1)!.

In the example, it is 5 people, so the answer is (5-1)! = 4! = 24.

and that was me as guest, forgot to put the id.