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# What is the probability of two books being standing in

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Manager
Joined: 24 Jun 2003
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What is the probability of two books being standing in [#permalink]  11 Aug 2003, 06:50
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What is the probability of two books being standing in adjacent places in a row of ten different books?
Manager
Joined: 10 Jun 2003
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Location: Maryland
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(1/9 + 16/9 + 1/9)/10 = 18/90 = 2/10 = 1/5.
Director
Joined: 03 Jul 2003
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Let us assume first one is A and next is B.

P(B/A) = 1/9 <-- A first and B second
P(A/B) = 1/9 <-- B first and A second

P(A and B toagther) = 1/9 + 1/9 = 2/9

Manager
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thought process [#permalink]  12 Aug 2003, 07:03
My thoughts were the following:

If one of the books is in the first position, then there is a 1/9 chance that the second book is adjacent. If one of the books is in positions 2 - 9, then there is a 2/9 chance that the other book will be one either side of it. If the first book is on the other end, position 10, then there is again a 1/9 prob that the other book is adjacent to it. I simply averages these 10 different scenarios to get 1/5.
Intern
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Stolyar,

9!*2/10!=1/5

Can u please explain how you worked out this problem!!!!!!!!!

Thanks
GMAT Instructor
Joined: 07 Jul 2003
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Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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p_malh wrote:
Stolyar,

9!*2/10!=1/5

Can u please explain how you worked out this problem!!!!!!!!!

Thanks

Imagine that the two book we want to keep together are taped together and treat them as one book. Now there are 9! ways to arrange these "9" books, each way keeping the books together. Now, of those two books, they arranged in 2 ways (BK1:BK2 or BK2:BK1). Hence there are 9!*2 ways to arrange them keeping the two books together and 10! total ways to arrange 10 book.

p = 9!*2/10!
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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