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We are given n distinct balls and m distinct boxes. m and n are non-negative integers....

We are given n distinct balls and m distinct boxes. m and n are non-negative integers. Every ball must be placed into a box, but not every box must have a ball in it. Each box can hold any number of balls. Let's also assume that the order in which we put the balls into the boxes does matter. (Ex: assume we have 2 balls, a and b, and 3 boxes, 1 2 and 3. two distinct distributions would be box 1 having a and b, and box 1 having b and a). How many ways are there to distribute the n balls into the m boxes?

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