If 14 persons are seated at a round table, then the number of
ways of selecting two persons out of them who are not
seated adjacent to each other is

First person can be chosen in 14 ways. After the first person is chosen, the second person cannot be chosen from a place adjacent to him. So two places out of remaining 13 cannot be selected. So 11 is the number of ways of selecting the second person.

 

Total number of ways = 14 * 11 = 154

First person can be chosen in 14 ways. After the first person is chosen, the second person cannot be chosen from a place adjacent to him. So two places out of remaining 13 cannot be selected. So 11 is the number of ways of selecting the second person. Total number of ways = 14 * 11 = 154