stand in a ring

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

stand in a ring

by sanju09 » Mon Feb 22, 2010 5:42 am

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

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Source: Beat The GMAT — Problem Solving | Mon Feb 22, 2010 5:42 am

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 am; Location: India; Thanked: 64 times; Followed by:6 members; GMAT Score:760

by harsh.champ » Mon Feb 22, 2010 5:48 am

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]

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