So, there is a deck of N cards ($N-2$ are blank, and $2$ are marked), you draw $5$ cards with each attempt, what is probability of picking 2 marked cards with the first and each new try? (The deck will be reshuffled, if there are not enough cards to draw.)
I tried to solve the problem using $_{N-5(x-1)}C_5$ ($x$ is number of attempts), but I don't understand how to subtract amount of right combinations from wrongs ones in this case.
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I think you have to put back in the deck every time you draw 5 cards, otherwise the situation is too complicated, as I wrote in the picture.