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

Umm... we don't do your homework for you. Where are you stuck?

experts exchange = not your personal geek

The summary of probability formulas in the "Summary of Probabilities" table on this wikipedia page will help you in solving the problem:

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

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.