Question

Fifteen persons, among whom are A and B, sit down at random on a round table. The probability that there are 4 persons between A and B, is A. 9! 14! B. 10! 14! C. 9! 15! D. none of these Select the correct answer from above options

Answer 1

Correct Answer - D Fifteen persons can be seated around a round table in 14! Ways. So, total number of ways =14! Four persons out of 13 persons (excluding A and B) can be selected in .13C4 ways. Considering these four persons and A and B as one individual there are 10 persons who can sit at a round table in 9! ways. Also, A and B can interchange their positions. So, total number of ways in which 4 persons can be seated between A and B is .13C4×9!×4!×2=2×13! Hence, required probability = 2×13! 14! = 2 14 = 1 7