Problem 3. While 52-card decks are most common in the United States today, other decks are
used elsewhere in the world or in history. For the purposes of this question, assume you are playing
with a 32-card Piquet pack, with cards numbered 7, 8, 9, 10, J, Q, K, and A in each of four different
suits (trèfles, carreaux, cœurs, and piques). Calculate the probability of each of the following hands,
assuming that you draw five cards from a well-shuffled deck.
(a) What is the probability of a royal flush (10, J, Q, K, and A all from the same suit)?
(b) What is the probability of a flush (all five cards are of the same suit)?
(c) What is the probability of a \"full house\" (three cards of one number, and two cards of another)?