# Probability of having picked every item from the set at least once after n turns, while picking 3 per turn

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.

• Presumably, you mean you choose three distinct items at random. – Thomas Andrews Apr 18 at 16:30
• This is a case for inclusion-exclusion. – Thomas Andrews Apr 18 at 16:32
• Yes. Included both. – DavidsKanal Apr 18 at 16:46
• Since you know that it is inclusion-exclusion, what do you need to use inclusion-exclusion? – Thomas Andrews Apr 18 at 17:18
• 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. – DavidsKanal Apr 18 at 17:59