Ten couples are going out to dinner. How many ways can they arrange themselves around a large, circular dinner table if they all must sit next to their partner? Notice that each couple consists of precisely two people, ergo there are twenty people in total. Show your steps. Solution The required steps are: 1)If we consider each couple as one unit then ten couples i.e ten units can be arranged in (10-1)! ways i.e in 9! ways since it is a circular arrangement we must fix one unit at first then the left 9 units can be arranged among themselves in 9! ways. 2)Now each unit again consists of two people and they can be arranged among themselves in 2! ways. So total number of possible arrangements is 9!*2!=725760..