Why is 9! correct? There are no additional rules implied in the question.
Imagine that 10 people are sitting at a round table. You can order them in 10! ways, but each time you shift everyone one seat to the right, it’s the same ordering. There are as many of these identical rotations as there are people. As such, you’re counting each unique arrangement 10 times when it should only be counted once. To account for this, we divide our total by 10; hence, \frac{10!}{10} = 9!