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Then fix some number M > N, and take M random numbers out from the generator. What is the probability, that these M numbers include each one of the numbers 1,2,3,...,N at least once?

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I know one person who buys some kind of candy where a small toy always comes with the candy. There is some number of different kind of toys out there, and this person became interested to know how many candy he/she should buy before getting them all. I found myself unable to answer it.