How many ways can 7 people be arranged to sit at a circular table?There are two interpretations to this question (a and b below).answer according to each of the interpretations a and b.

a) First interpretation:Find the number of different ways 7 people can be seated on 7 different chairs that are at the table.

For example, if there were 3 people and 3 different chairs (say wooden ones made out of walnut, cherry and oak) the number of ways to have different people on different chairs is 6.

b) Second interpretation:Find the number of different arrangements of people.Assume all chairs are identical since we do not care who sits on any particular chair.What we do care about is who is at one's right hand and who is at one's left hand.Each arrangement differs from all others regarding who is sitting to the right of whom and who is sitting to the left of whom.

For example, if there were 3 people, the number of different arrangements is 2.