SOLUTION: In how many ways can 10 runners finish a race first, second, or third? I don't understand how to even set this up to solve it!

Question 439480: In how many ways can 10 runners finish a race first, second, or third?
I don't understand how to even set this up to solve it!
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
In a 10 man race, how many runners have the chance to finish first?
answer 10.
Now that 1 person is first, how many runners could be second? Well, there are still 9 runners left, and any one of hem could be second.
Answer 9.
How many can be third? Using the same idea as above, once one person is first and another is is second, that leaves 8 people still running and trying for third. So how many can be in third?
Answer 8.
Now you need to do the math

So there are 720 different ways
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