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# Five thousand runners will participate in the Mountain Marathon. Each runner will randomly be given a different number from 1 to 51000 to wear during the race. What is the probability that the number

Posted on 2010-11-08
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Five thousand runners will participate in the Mountain Marathon. Each runner will randomly be given a different number from 1 to 51000 to wear during the race. What is the probability that the number of a second-place finisher will be both greater than the the number of the third-place finisher and less than the number of the first-place finisher? (Assume noties) Express your answer as a fraction.
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Question by:praveen_katta
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Expert Comment

ID: 34087884
Umm... we don't do your homework for you. Where are you stuck?
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Expert Comment

ID: 34087897
experts exchange = not your personal geek

http://en.wikipedia.org/wiki/Probability#Mathematical_treatment
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LVL 37

Expert Comment

ID: 34087990
I'd actually approach this as a permutations problem. You know there will be three numbers. You know they are unique. How many ways can they be arranged? How many of these ways satisfy the description? Are all the permutations equally likely?

If this makes no sense, ignore it. If it does, use it to make the problem super easy.
That's all the help I feel comfortable giving. Your prof and your textbook are good resources too.
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Accepted Solution

deighton earned 500 total points
ID: 34092544
the problem here is to see the wood for the trees.  What you are interested in is only the first 3 finishers, and they all have a different number.  It doesn't matter what the numbers are, can you see that?  It will always be possible to order the numbers of the top 3.

Think about the top three runners, if their numbers were 1,2 & 3, so they are asking you the chances of the finish being

3,2,1

how many ways could you arrange that?
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