So if 6 married couples are seated around a circular table, how many ways can they do this if husband and wives must be seated side by side?
I figured if there are 6 couples there must be 12 individuals. From there we must find the number of 2 element subsets of these 12 individuals such that '12 choose 2' but since there are 6 couples we must divide by 6! is my thinking right?
Best Answer
Strong hint
Seats in a circle are taken as unnumbered unless otherwise specified.
n people can be seated in $(n-1)$ ways in unnumbered seats in a circle.
With $6$ individuals it would be 5! ways, but these are $6$ "together" couples,
and each couple can be "flipped $[Aa\;\; or\;\; aA]$ so multiply by 2 for each couple.