# In a horse race, how many different finishes among the

In a horse race, how many different finishes among the first three places are possible for a ten-horse race?
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Step 1
Assuming all horses have an equal chance of winning, there are 10 horses which can come in first, then, there are 9 remaining horses which can come in second, and finally, there are 8 remaining horses which can come in third.
Step 2
The number of different finishes for the first three places are:
$10×9×8=720$