Fifteen persons among whom are A and B, sit down at random at a round table. The probability that there are 4 persons between A and B is:

None of these

Fix 'A': Now B will have '2' positions. Choose 4 people out of 13 and place them in between A and B and arrange rest 9 people amogst themselves.

⇒ Favorable ways = $2×({^{13}C}_4.4!)×9!$ and total ways = 14!

⇒ P(required) = $\frac{2×{^{13}C}_4×4!×9!}{14!}=\frac{1}{7}$