# Applying Counting Theory

Provide a numerical answer to each of the following questions and also show the calculations you used to find the answers.

1. How many different ways can 30 runners place in an Olympic qualifying marathon?

2. If only the eight fastest runners advance to the Olympics; how many different ways can the eight fastest runners be chosen from the whole field of 30 runners?

3. If the runner in first place receives a gold medal, the runner in second place receives a silver medal and the runner in third place receives a bronze medal; how many different ways can the three medalists be chosen from the whole field of 30 runners

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Is this homework? What have you tried? –  Colin McQuillan Feb 12 '12 at 20:11
Why should we provide you numerical answers; and on top of that, show you calculations. Please be polite - you're asking for help in some form and you cannot order us to do things for you! -1 –  user21436 Feb 12 '12 at 20:20
For 1, I expect ties, possibly of a multiple character, are not allowed. If they are, things get much more complicated. It should be clear that $30$ people can be arranged in a row in $30!$ ways. –  André Nicolas Feb 12 '12 at 20:38
Unlike some, I’m not much bothered by the form of the question, but these are very easy questions; if this is for a course with a textbook, I’d be very much surprised if the book didn’t have examples very similar to these problems. Thus, it’s very hard to guess where you might be having trouble. –  Brian M. Scott Feb 12 '12 at 21:25
@KannappanSampath, don't take it too personally; he's obviously quoting from some homework assignment, and hence the inappropriate (for this forum) phrasing. –  Gadi A Feb 12 '12 at 21:44

Ironically enough this question was posed in one of my own homework assignments this week. It's not hard at all to solve, the user just need to read their textbook for the week and bone up on combinations, permutations, and factorial notations.

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Don't Know if I'm right, so check yourself on it. Think it's 30x30 for the first.
P(r,n) is P(30,8) or 30!/22! (seems way big.so AGAIN "check it").
I think it's P(30,3). you gotta do the n!/(n-r)!=30!/(30-3) = 30x29x28/1 =24360 AGAIN I'm not sure as I'm trying myself. Any helpful response to my work would be appreciated

Thank you

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Q#2: Do the 8 have to be ordered to get into the final? I guess as long as the person gets in the first 8, whether he's 1st or 8th doesn't matter much -- that is to say, $C_{30}^8$. By the way, you chould use $<- block me up ->$ for formulae/expressions. –  FrenzY DT. Aug 14 '12 at 4:55
How did you get your answer for the first? Answers need to be thorough and for homework assignments, you should not give complete answers but hints. –  cheepychappy Oct 2 '12 at 13:18