I know the solution to this problem is (n-1)!. If it was a line we would have used n! for each spot as we care about order and we cannot choose a person more than once. I also know that the way you get to this number is because it is possible to rotate the circle through n possible combinations which are essentially the same. Here, i get a bit confused though. At this point, why not subtract these n (or maybe n times n for each person we choose to put at a specific chair) possibilities from the total? why do we divide by n?
p.s. I know about the explanation involving the first person as a pivot. I am mainly having a hard time with the division of n.