How many different ways can you seat 10 men and 10 women around a circular table if you need to alternate men and women?

Shouldnt the answer be 10!*9!*2?

You set either the man or woman static and populate the remainder of the table. However there are 2 different choices which can start the sequence, either a man or a woman.
Since I started the sequence with a man, the second option would be to start the sequence with a woman, hence the *2 in the above equation. Please confirm?

Since it is a circular arrangement, the answer is 9! * 10! regardless of whether we start with man or a woman. The reason for this is that, in a circular arrangement, it is only the relationship of one person to another that matters, not the starting position.

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