The Plain Straight

A 5-card hand is dealt uniformly at random from a standard 52-card deck. A straight is five cards of consecutive ranks. The ace may play high (10-J-Q-K-A) or low (A-2-3-4-5) but does not wrap around (Q-K-A-2-3 is not a straight). What is the probability that the hand is a straight but not a straight flush, so its five cards are not all of the same suit? Give your answer as a reduced fraction.

• distributions

Source: Standard poker-hand probability exercise from introductory probability texts. Statement written for AxiomIQ.