Let's say I have a set of 100 items. Each turn, I pick three items at random, note which ones I've picked, and put them back. What is the probability I've picked every item at least once after $n$ turns? The only statement I can make right now is that $n \geq \frac{100}{3}$ in order for the probability to be non-zero.

  • $\begingroup$ Presumably, you mean you choose three distinct items at random. $\endgroup$ – Thomas Andrews Apr 18 at 16:30
  • $\begingroup$ This is a case for inclusion-exclusion. $\endgroup$ – Thomas Andrews Apr 18 at 16:32
  • $\begingroup$ Yes. Included both. $\endgroup$ – DavidsKanal Apr 18 at 16:46
  • $\begingroup$ Since you know that it is inclusion-exclusion, what do you need to use inclusion-exclusion? $\endgroup$ – Thomas Andrews Apr 18 at 17:18
  • $\begingroup$ I don't know that it is inclusion-exclusion. In fact, I don't know what that is. But I'm quick to trust people so I added it as a tag. $\endgroup$ – DavidsKanal Apr 18 at 17:59

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