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.