A five-card poker hand is dealt at random from a standard 52-card deck. Note the total number of possible hands is C(52,5)=2,598,960. Find the probabilities of the following scenarios:
(a) What is the probability that the hand contains exactly one ace?
(b) What is the probability that the hand is a flush? (That is all the cards are of the same suit: hearts, clubs, spades or diamonds.)
(c) What is the probability that the hand is any straight flush? (We are including royal flush, so we want all five cards of the same suit, and with consecutive rank like 2,3,4,5,6.)