Question: How do you check for a drawn card being any card other than a certain card when drawing cards WITHOUT replacement, but also apply conditions on the rest of the cards. To make things more complicated, the frequency of each card in the deck is different.
Context:
Assume I have a deck of cards, with the frequency of each card being different.
When drawing X cards where order does not matter and no replacement, what is the chance of getting:
-At least 1 of each of (A, B, C) AND the remaining cards being any card (including A, B, C) except card Z
-At least 2 different cards of (A, B, C) AND the remaining cards being any card (including A, B, C) except card Z
The problem is combining different conditions when there is no replacement. Does order here matter or no? How do I combine different conditions? I thought P(Z') - P(A'Z') - P(B'Z') - P(C'Z') but I am certain there is overlap between them, as A'Z' also includes some of B'Z'. Also, how is it possible to check for having at least two different cards?