Q:Three engineers and nine coucillors have a meeting around a circular table. If three coucillors are between each engineer, find the number of possible seating arrangments.

the circle permutations formula is $\displaystyle (n-1)!$

the answer is Arrangements: $\displaystyle 2! \times 9!$

whats wrong with $\displaystyle 3!\times8!$, could someone explain why this is wrong, why is it not adhering to the conditions of the question?

Thanks