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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

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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praveen_katta
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Commented:
Umm... we don't do your homework for you. Where are you stuck?
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Commented:
experts exchange = not your personal geek

http://en.wikipedia.org/wiki/Probability#Mathematical_treatment
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Commented:
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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progCommented:
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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