Actually, no. The number depends on the position at the table—rotations are distinct.
For 3 couples:
Mrs A must sit between Mr B and Mr C. Mr B can be on her left or her right, 2 possibilities. After those two seats are chosen, everyone else’s seat is determined.
But there are 6 places Mrs A might sit. Hence, for 3 couples there are 12=2x6 possible seatings, including rotations.
For 3 couples:
Mrs A must sit between Mr B and Mr C. Mr B can be on her left or her right, 2 possibilities. After those two seats are chosen, everyone else’s seat is determined.
But there are 6 places Mrs A might sit. Hence, for 3 couples there are 12=2x6 possible seatings, including rotations.