I'm trying to work out some statistics for a game I'm working on, but can't wrap my head around some of the statistical concepts.
To make a generic case along the lines of what I'm trying to do:
Let's take a standard deck of 52 cards. What is the probability that, if I draw 7 cards, at least 3 of them are hearts, and at least 2 of them are different non-heart faces (i.e. they can't both be kings, or both be queens, etc.)?
It's not a perfect analog for what I'm actually doing, but it's close enough.
I think I've come up with an answer, can somebody confirm if this is correct?
3 hearts = 13 × 12 × 11
First non-heart face = 9
Second non-heart face = 6
All criteria together = 13 × 12 × 11 × 9 × 6