Disclaimer: I am not in a mathematics field or a mathematics professional.
I'm interested to know how many random draws it would take to have a particular chance (50%, 75% and 90%) of getting 5 specific results (out of a pool of 12 possible results) at least once each, assuming that it is possible to obtain each result more than once and that each result is equally probable.
Eg. How many times would you have to roll a 12-sided die before you had a 50% chance of rolling at least one each of the numbers 1, 2, 3, 4 and 5? How many rolls for a 75% chance? How many rolls for a 90% chance.
I know this is a variant of the coupon collector problem, but my maths is nowhere near good enough to work on the problem or to even follow many of the explanations I've found online.
While I'm primarily interested in the "5 out of 12" scenario mentioned above, I'm also curious what the formula would be for "X out of Y" where X is the number of specific results that are desirable and Y is the total number of possible results.