In how many ways can 5 people from a group of 6 people be seated aroun

I don't understand why seating 5 people around a circular table is (5-1)! and not 5!. Can anybody explain? Does it have something to do with the table being circular?

If we were asking how many ways there are to line the five people up from left to right, we would have left, next-to-left, middle, next-to-right, and right. You'd have five choices to fill the first slot, four to fill the second, three to fill the third, two to fill the fourth, and one to fill the fifth. So, 5*4*3*2*1, which is 5! HOWEVER, we are looking at a circular table. If everyone is seated and just gets up and moves one seat to the left, we don't want to count that as a new arrangement. It's the same arrangement, just rotated one seat to the left. So how do we solve it? Let's say we seat person A and then work to the left, there are now four choices to fill the seat to the left of A, three choices to fill the seat two to the left of A, two choices to fill the seat three to the left of A, and one choice to fill the last seat. So, 4*3*2*1, which is (5-1)!.