In how many inequivalent ways can 8 people be seated at a round table? How many different arrangements are there of eight people seated at a round table, where two arrangements are considered the same if one can be obtained from the other by a rotation?

Imagine that the $8$ people take their seats one at a time, from shortest to tallest. Since orders equivalent by rotation are considered the same, it doesn’t matter where the $A$, first person sits; the arrangement is determined by how the others are seated in relation to $A$. They can then be seated in any order clockwise around the table from $A$’s left. How many permutations of those $7$ people are there?