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What are the possible outcomes when a 'm' sided die is thrown 'n' times? and What are the possible outcomes when 'n' dice are thrown at a time having 'm' sides each?

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The number of outcomes for the two scenarios are precisely the same:

$$m^n\;\text{ outcomes}$$

That is, it doesn't matter whether we throw a die $n$ times, or if we throw $n$ dice all at once, as long as in both scenarios, we use the same values for $m$ and $n$.

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