I'm having troubles with solving this question:
We have 6 people. In how many ways we can put them in a line?
-The answer is $720$, because $6!=720$.
We want to put them in circle with 6 seats.
-The answer is $5!=120$.
In circle with $10$ seats?
-The answer is $15120$, but I can't figure it out why is that so.