Consider a collection of 5 people. How many more ways can these people be arranged in a line than around a circular table?

Answer 1

arrangements in a line = 5! = 120

around a circle, with no specified position around the table = 5! / 5 = 4! = 24

e.g. for any arrangement of the 5 people around the table, everybody could get up, move once to the left, and the arrangement would not change, etc . We could do this 5 times without altering the arrangement.
That is why I am dividing 5! by 5