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if 10 students enter projects in the art show, how many different ways can they come in 1st, 2nd, and 3rd place?

would you go 10^3

This is not a trig question.
Neither of those answers is correct.
After making one of ten possible choices for first place, there are 9 possible choices for second place, etc.
The answer is 10*9*8 = 720

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