There are 3 couples sitting randomly round a 6-seater circular table. What is the probability that all the husbands and wives sit next to each other?
First wife, say, takes any of the six seats. That leaves 2/5 seats where her husband can sit next to her. Second wife, say, can take any of the four remaining seats. There is then only 1 seat out of the remaining 3 where her husband can sit next to her AND leave two empty adjacent seats for the last couple.
So the answer is 2/5 * 1/3 = 2/15.