# Probability Urn Question

An urn contains n balls, all different colors. A person draws a ball randomly, records the color before replacing it. The person must record all colors in order to receive a large prize. If m colors have been recorded so far, what is the probability that it will take exactly x draws to get a new color?

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Hint: Think of each draw as a Bernoulli trial, with "success" meaning you get a colour that's not one of the $m$ you've already seen.