The population of 5 card draw hands, consisting of 52 choose 5 or 2598960 elements, is pretty straightforward both mathematically and statistically.
So of course ever the geek, I just had to attempt to show her how probability and statistics converge. In addition to explaining the “combinatorics” of the counts and probabilities, I undertook two computational exercises. The first was to delineate all possible combinations of 5 card draws from a 52 card deck, counting occurrences of relevant combinations such as 2 pair, a straight, or nothing in a cell loop.
Steve has made his notebook available for us.