Round table

There are $7!$ different ways to order seven people. For each of these orders, there are $7$ different seating arrangements that have this order that we are considering equivalent. $\frac{7!}{7} = \boxed{6!}$

The first person can sit in any place, because the seats are not numbered, then there are $6!$ arrangements for the six other people .

Because ,

Now we will deal with the seats according to the place of the first person , for example we can say $2$ seats right the first person ...

So there are $6$ different people and $6$ "different seats "( we will deal with them as they are different) .