[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

A poker hand is a set of 5 cards randomly chosen from a deck

of 52 cards. Find the probability of a

• royal flush (ten, jack, queen, king, ace in a single suit).
• straight flush (five in a sequence in a single suit, but not a royal flush).
• four of a kind (four cards of the same face value).
• full house (one pair and one triple, each of the same face value).
• flush (five cards in a single suit but not a straight or royal flush).
• straight (five cards in a sequence, not all the same suit). (Note that in straights, an ace counts high or low.)