Help with kind of weird odds calculations
Hello. I'm looking to perform a study on a site's shuffling and help with any of these calculations would be extremely appreciated.
It might be painfully obvious but I want to make sure I do this right, and I'm a bit stumped.
How would I calculate the odds
of the community (basically any random 5 cards) having at least one pair among it? I can figure it out if it's one specific card, but as far as there being one pair among any of the 5 cards, I'm not quite sure how to go about calculating it.
Similarly, I want to know how I'd calculate the odds of the community (any 5 cards) holding three of the same suit. The suit does not matter.
And with these two odds, could I then figure out the odds of any 5 cards having EITHER a pair or flush draw?
I don't know if these are difficult calculations or if they're just more obvious than I'm seeing, but I thank anyone who will help.