20 persons are sitting in a particular arrangement around a circular table. Three persons are to be selected for leaders. The number of ways of selection of three persons such that no two were sitting adjacent to each other is

The total number of ways of selection without restriction is  20C3.The number of ways of selection when two are adjacent is 20×16C1. The number of ways of selection when all the three are adjacent is 20 . The required number of ways is 20C3−20×16−20=20×19×186−20×16−20=20[57−16−1]=20×40=800