Question

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

Answer 1

Total number of students = 15
talkative students = 2

Left students = 15 - 2 = 13
Thus

ways they can be seated = 13 /15

Answer 2

Answer:

$13\times 14!$

Step-by-step explanation:

Total no. of students are 15

Talkative students = 2

When one talkative is fixed so, 14 places are remaining

So, arrangement of those 14 students = 14!

Now the second talkative student ha total 13 places to sit but we are given that talkative students should not sit together .

So, he cannot sit on the sides of another talkative students

So, he has 13 places to sit

So, No. of ways can 15 students be seated in a row such that the 2 most talkative children never sit together = $13\times 14!$

Hence there are  $13\times 14!$ ways .