If all hands are equally likely, the probability of a single pair is obtained by dividing by 5). This probability is Missing: functions.

frequencies for 5 - card poker hands as follows: # define RANK(card) ((card) % 13) inc function increments hand to the next combination.

49 possible 4th cards you could get. 48 possible 5th cards you could get. That makes the number of different ways. that you can be dealt a 5 card poker hand is. Missing: functions.
Independent One 1 bet vegas and Independent Experiments. This is not exactly the property we are looking for, but it seems to fit the job. See also: sample space and event probability theory. The crude information-theoretic lower bound for the maximum hand ID is. The number of ways of performing each step is also given. This means that the solutions are far from being optimal. Don't scroll through the code if you want to avoid spoilers, the first elements are hardcoded.