Question

15 persons among whom are A and B, sit down at random at round table. The probability that there are exactly four persons between A and B is

(a)   9!/14! 

(b) 10!/14! 

(c)  2.9!/14! 

(d) 2.13!/14!

Answer 1

Correct option(d) 2.13!/14!

Explanation:

15 persons can be seated round a table in 14! ways. If 4 persons are to be included between A and B, they can be arranged in ¹³C₄  x 4!  ways, now total number of arrangements is ¹³C₄ x 4! × 9! × 2! = 2.13!

Hence the probaility is 2.13!/14! = 2/14 = 1/7