Math questions from any Manhattan Prep GMAT Computer Adaptive Test.
kelsey.klaver
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combinatorics: In a race with 10 competitors...

by kelsey.klaver Tue Jul 15, 2014 10:23 pm

In a race with 10 competitors, the first-place finisher receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. If there are no ties, in how many different ways may these three medals be awarded?

Answer choices:
35
120
720
840
604,800

I'm sure this is a basic combinatorics question, but I'm curious to know something: could you show me the combinatorics for three medalists, as well as for ten medals, if they were to be awarded to all runners?

Thanks in advance,
Kelsey
RonPurewal
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Re: combinatorics: In a race with 10 competitors...

by RonPurewal Wed Jul 16, 2014 9:29 am

Three medalists = the original problem.
The original problem has an answer key, which should already contain what you're asking for. So, the best way to answer that part of your question is to turn it around: What don't you understand in the answer key?
RonPurewal
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Re: combinatorics: In a race with 10 competitors...

by RonPurewal Wed Jul 16, 2014 9:29 am

If everyone gets a (different) medal, the problem becomes the same as asking for the number of ways to scramble 10 different items. E.g., it's the same as the number of ways to arrange 10 books in order on a shelf.
Do you know how to do that sort of thing?