So I'm trying to figure a few things out with probability/counting. These a probability questions, but my understanding of the counting behind them is a little fuzzy still.
For example, The probability of getting 3 of a kind out of a 5 card poker hand is:
COMBIN(13, 1) to choose 1 kind of out the 4 kinds
COMBIN(4, 3) to choose 3 cards out of the 1 kind
COMBIN(12, 2) to choose the 2 kinds for the last 2 cards (the first card took 1 kind already, so it's 12 instead of 13)
(COMBIN(4,1))^2 to choose the 2 cards out the the last kind(s)
So, the answer is: (COMBIN(13,1)*COMBIN(4,3)COMBIN(12,2)(COMBIN(4,1))^2)/(COMBIN(52,2))
How would this change if I were to look for AT LEAST 3 cards of the same kind instead of EXACTLY 3 cards of the same kind?