Why the answer to n places over a round table is n! to chair that is signed and not the answer (n-1)!?
A round table table is unordered. That is if we seat $n$ people a a round table, if we rotate table nothing about the order of the people changes. Thus we must account for the effect of rotations.
If we take one of that group say the tallest and seat her/him anywhere at the table. Now with respect to that individual the table is now ordered (to his right or her left) So there are now $(n-1)!$ ways to seat the remaining people. So you are correct it is $(n-1)!$