But sitting N people around a table there is no starting (left-hand most) person.
If we wanted to we could designate a ‘starting’ person in N ways.
Thus there are only different ways to do this.
Here is another way to look at this problem.
At a circular table with N seats, pick one to be the head of the table.
Select one person to be seated there.
Now there are people left.
Starting at the right-hand side of the head-seat, there are ways to seat the remaining people.