Permutations without Repetition

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Permutations with repetition was a simple formula: NxN... or NE. But what happens if you cannot reuse any elements? For example, let's say only 3 students entered the poetry contest you are judging. How many possible ways are there to award 1st, 2nd and 3rd place?

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The ForceBall Lottery uses 12 balls numbered 1-12. Each ball spins in a machine until it pops out. How many possible orders are there (for the balls to pop out) in the ForceBall Lottery?

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