A poker deck consists of cards ranked 2,3,4,5,6,7,8,9,10,J,Q,K,A, (13 different ranks) each in four suits, for a total of 52 distinct cards. A pinochle deck consists of two copies each of cards ranked 9,10,J,Q,K,A, each in four suits, for a total of 48 cards (24 pairs of identical cards).What is the probability that a five-card poker hand drawn from a pinochle deck contains no duplicate cards?
