How many ways can seven people sit around a circular table? How many ways seven people can sit around a circular table?
For first, I thought it was $7!$ (the number of ways of sitting in seven chairs), but the answer is $(7-1)!$.
I don't understand how sitting around a circular table and sitting in seven chairs are different. Could somebody explain it please?

In a circular arrangement we first have to fix the position for the first person, which can be performed in only one way (since every position is considered same if no one is already sitting on any of the seats), also, because there are no mark on positions.
Now, we can also assume that remaining persons are to be seated in a line, because there is a fixed starting and ending point i.e. to the left or right of the first person.
Once we have fixed the position for the first person we can now arrange the remaining $(7-1)$ persons in $(7-1)!= 6!$ ways.
