Six couples are to be seated around a circular table, in 12 chairs. How many ways can this be done if each couple is together?
Circular arrangements have a different count. There are $(N-1)!$ ways to arrange $N$ distinct items in a circle.
In this problem the six couples sitting together can be though of as six distinct items. But each couple can be seated in two ways(husband to the wife's right or visa-versa.) So what is the total?