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Choosing First, Second, and Third Place Winners

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Using all 30 runners in each of the following cases, how many different outcomes are possible?
We are reporting on the ranking of each runner in the marathon.
This is a qualifying marathon for the Olympics and only the fastest eight runners advance.
The top three runners will receive gold, silver and bronze medals.

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Solution Summary

This solution shows how to calculate the number of outcomes for a marathon, as well as the number of ways first, second, and third place winners can be chosen using combinations and permutations.

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It does not matter in what order the 8 runners are chosen from the pool of 30. So, we use ...

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