text: permutation? at a dinner party, 5 people are to be seated around a circular table. two searting 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? the answer is 24  5 people can sit in 5 seats in 5 p 5 or 5! ways =120  but when the chairs are arranged around a circular table, the number of arrangements = 120 / 5 = 24  detailed explanation :-   the following 5 arrangements are included when we do 5!  a b c d e b c d e a c d e a b d e a b c e a b c d  but in the above cases the positions of the people relative to each other are the same.  therefore, we need to divide the answer by 5