** I FIGURED OUT 15 out of 16 cases. I don't understand the last case of RUNT. Anyone helps? I recently went to a math event and one person presented a weird card deck, consisting of 13 ranks and 5 suits, yielding a total of 65 cards. I later found out this card deck is here.
What I couldn't figure out is the counts of 5-card poker with super hands (these are hands consisting of cards from all five suits). The probability is easy to figure out, since it is the count divided by the number of ways to get 5 cards ($8,259,888$ in this situation). I worked out the first two, 5-of-a-kind and straight flushes but couldn't go further. Any suggestion is really appreciated.