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.

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- Feb 18th 2013, 05:24 AMkastamonuround table
**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. - Feb 18th 2013, 06:18 AMPlatoRe: round table
- Feb 18th 2013, 06:57 AMkastamonuRe: round table
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.

- Feb 18th 2013, 07:17 AMPlatoRe: round table

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.

$\displaystyle 6\cdot 4\cdot 2=48$. - Feb 18th 2013, 09:17 AMkastamonuRe: round table
What happens if we want all the couples to sit seperately?

- Feb 18th 2013, 09:24 AMkastamonuRe: round table
There are 4 married couples. If we think them as 1 person they can be arranged in 3! They will change places between themselves in 2! ways. TRhere are 4 couples and this makes 2!2!2!2!3!

- Feb 18th 2013, 11:00 AMPlatoRe: round table