Problem Solving

A and B stand in a ring with 10 others. If arrangement of 12 persons is at random then what is the probability that there are exactly 3 persons between A and B?
(A) 2/11
(B) 3/11
(C) 5/21
(D) 8/21
(E) 16/21

sanju09 wrote:A and B stand in a ring with 10 others. If arrangement of 12 persons is at random then what is the probability that there are exactly 3 persons between A and B?
(A) 2/11
(B) 3/11
(C) 5/21
(D) 8/21
(E) 16/21

let 3 persons be between A and B.
Those 3 persons alonwith A and B can be considered as one entity lets say X.
Hence we have 7 persons,X -total = 8
Arrangements = 7!(since circular permutations) x 3! x 2! x 10C3(arrangement inside X)

Sample space arrangements = 11!(since circular permutations)

[spoiler]Ans. =7! x 3! x 2! x 10C3/11! =2/11 A[/spoiler]