In how many ways can 15 students be seated in a row such that the 2 most talkative children never sit together?

$$14 ! \times13$$

Explanation

First we have to place 14 students leaving one talkative student so 14! for placing the 14 students. Now we have 15 places vacant to place the 2nd talkative student. But as 1st talkative student is already placed places adjacent to him are not to be used so 13 places left. Answer is $$14 ! \times13$$