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# Imagine a parking lot with 999 cars with license plates

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GMAT Instructor
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Imagine a parking lot with 999 cars with license plates [#permalink]  12 Aug 2003, 06:45
Imagine a parking lot with 999 cars with license plates numbered from 001 to 999 and no two cars having the same license plate number. At 5pm, they all leave the lot one by one. What is the probability that the license plate numbers of the first four cars to leave are in increasing order of magintude?
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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

Last edited by AkamaiBrah on 13 Aug 2003, 07:14, edited 1 time in total.
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AkamaiBrah wrote:
Imagine a parking lot with 999 cars with license plates numbered from 001 to 999 and no two cars having the same license plate number. At 5pm, they all leave the lot one by one. What is the probability that the license plate numbers of the first four cars to leave are in increasing order of magintude?

The # of the first car can be anywhere, but the AVERAGE of all of the places it could be is right in the middle, so the average chances of the second car being greater than this value is 1/2.

Now the third car has to be above the second, and the chance of this is 1/4. And finally, the fourth must be still above that so 1/8.

1/2 * 1/4 * 1/8 = 1/64
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Is it 999C4 * (1/2)^4 ?
Manager
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Is it 999C4 * (1/2)^4 ?

Kpadma, your answer equals way over 1, with 1 being a certain probability. I don't think that passes a sanity check.
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AB,

Here I come charging again.

P = (997)^2 / (8 * 999 * 998 ) = (approx) 1/8

I think I may be close to the answer, but not sure it the correct answer.
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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I think I may be close to the answer, but not sure it the correct answer.

sounds like yogi berra.
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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

GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
Followers: 13

Kudos [?]: 52 [0], given: 0

AkamaiBrah wrote:
I think I may be close to the answer, but not sure it the correct answer.

sounds like yogi berra.

Any four cars have an equal chance of leaving the lot first, so we can concentrate on just one specific bunch of four cars. (Whether there are 999 or just 4 cars in the lot is irrelevant). For a given set of four cars, they can leave the lot in 4! or 24 ways, only one of which the license plate numbers will be in increasing order. Hence, the answer is 1/24.
_________________

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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A nice trick! Remember a question with six letters to be distributed among six envelopes? What is the probability of having them all distributed correctly? 1/6! Again, there is the only right case.
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