Poker Hands: counting

Assume that each of Poker hands are equally likely. The total number of hands is

\[\begin{pmatrix} 52 \\5\end{pmatrix}\]

Find the probability of being dealt each of the following:

  1. a straight flush ( all cards of the same suit and in order)
  2. a regular straight (but not a flush)
  3. two of a kind
  4. four of a kind
  5. two pairs (but not four of a kind)
  6. a full house (a pair and three of a kind)

In all cases, we mean exactly the hand stated. For example, four of a kind does not count as 2 pairs and a full house does not count as a pair or three of a kind.


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