I receive this problem today, from Stan Wagon’s Problem of the Week. I slightly reword it:
You are playing stud poker (5 cards dealt, no exchanging of cards) with a few friends and a standard 52-card deck. It’s your lucky day and by some miracle you are guaranteed to end up with a full house, but only if you correctly choose the best full house. Which full house should you choose? (i.e., which full house has the highest probability of winning?)
I gave this problem some thought. It is not as easy as it looks. What is the answer?