[SOLVED] Counting Seating Arrangments of Couples at a Round Table I'm reading this example in my probability book which is I'm not understanding. It says: There are 19! ways of arranging 20 people around a table. The number of arrangements that result in a specified set of n men sitting next to their wives can most easily be obtained by first thinking of each of the n married couples as being single entities. If this were the case, then we would need to arrange 20 - n entities around a round table, and there are clearly (20 - n - 1)! such arrangements. There are 10 married couples by the way. The "20 - n entities" part is bugging me. Shouldn't that be 10 - n, given that there are 10 entities/married couples. I also don't understand how the (20 - n - 1)! part follows.