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[#10] 2 Min. Challenge : Cars - Probability

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Praetorian
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[#10] 2 Min. Challenge : Cars - Probability [#permalink] New post   08 Mar 2004, 21:35
Rules

1. Time yourself
2. Solve this problem on a sheet of paper [ under 2 mins, if possible]
3. type in your solution and the time, if possible.

Imagine a parking lot with 500 cars with license plates numbered from 001 to 500 and no two cars having the same license plate number. At 6 pm, 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?

1/8
1/24
1/64
1/128



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kpadma
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Re: [#10] 2 Min. Challenge : Cars - Probability [#permalink] New post   08 Mar 2004, 22:04
Ans: 1/24

Ways to arrage four cars = 4! = 24
only one way to have the numbers in increasing order

P = 1/24
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anandnk
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Re: [#10] 2 Min. Challenge : Cars - Probability [#permalink] New post   09 Mar 2004, 06:00
This is the best question. I could not solve it. But I agree with kpadma's solution.
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Praetorian
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Re: [#10] 2 Min. Challenge : Cars - Probability [#permalink] New post   09 Mar 2004, 11:37
praetorian123 wrote:
Rules

1. Time yourself
2. Solve this problem on a sheet of paper [ under 2 mins, if possible]
3. type in your solution and the time, if possible.

Imagine a parking lot with 500 cars with license plates numbered from 001 to 500 and no two cars having the same license plate number. At 6 pm, 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?

1/8
1/24
1/64
1/128


I am quoting a legend here :

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.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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gmatclubot
Re: [#10] 2 Min. Challenge : Cars - Probability [#permalink]
09 Mar 2004, 11:37
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
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