4 married couples sit at a round table. How many ways can they sit if each husband must sit opposite his wife?
3!3.2! is my answer.
3!.16 . If we think four couples as one person we can place them in 3! ways. 2 couples will be ordered between themselves and there are 4 couples this makes 16. But your nswer is better. Many Thanks.
I don't know where you are getting your model, but it is wrong.
Draw a regular octagon. There vertices are the eight chairs.
It is not ordered until one couple is seated.
Seat couple A anywhere, but man and wife are at opposite vertices.
Now the table is ordered.
There are six seats left. Seat wife B in any one of them. Then man B has only one place to be seated, at the opposite vertex from wife B.
$\displaystyle 6\cdot 4\cdot 2=48$.