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I am trying to calculate the amount of times (experiments) I need to perform were I choose $k$ items from a list of $n$ items so that I have a probability $P$ that each of the n items was selected at least once.
I attacked the problem by starting small and saying I have 5 items and each experiment consists of drawing two of them (without replacement). After the first experiments I reasoned that I have 100% probability that there are 3 items not selected yet. I proceeded to calculate the probability that after the second experiment I have three, two, or one items not selected. And so on with the third experiment and more.
Unfortunately, I am having trouble generalizing this approach to $n$ and $k$ and to a number of experiments $m$.
I suspect there is a good chance that this is a duplicate. If so can someone please point me in the right direction?