In how many different ways $7$ students can sit at a round table? > In how many different ways $7$ students can sit at a round table? I can't get my head around this one. I think there's something with the fact that the table is round. The answer in my text book is $720$.

The number of ways to arrange $n$ distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is

$$P_n=(n-1)!$$ The number isn't the usual factorial $n!$ since all cyclic permutations of objects are equivalent because the circle can be rotated $n$ ways, and thus it is $\frac{n!}{n}=(n-1)!$.

Thus, the answer given is $6!=720$.