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stand in a ring

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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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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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