Hello, aonin!

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 answer is: .

The basic arrangement looks like this (not including rotations):

. .

The first engineer can sit in any chair (it doesn't matter).

The second engineer has a choice of either of the other two E-chairs.

The third engineer has only one choice: the remaining E-chair.

. . Hence, the engineers can be seated in ways.

Then the nine "coucillors" can be seated in ways.

.Answer: .