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Given a 52 card deck how many 5 card stud poker hands are there?

5 card stud poker is when 1 card is dealt face down and 4 face up. I guessed it would be $\frac{P(52,5)}{4!}$ because the order of the face up cards doesn't matter, but Schaum's says it's just $P(52,5)$.

Why?

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    @BrianM.Scott Thanks. I am always confused by those. It keeps me wondering, why won't we create yet another symbol for $\binom{n}{k}k!(n-k)!$.2012-03-13

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Revised: The order in which the cards are dealt matters, because there is a round of betting after each up card appears. Thus, there is a difference between getting the ace of spades as a hole card followed in order by $\diamondsuit Q,\diamondsuit 10,\diamondsuit 3,\clubsuit Q$ and the same hole card followed in order by $\diamondsuit Q,\clubsuit Q,\diamondsuit 10,\diamondsuit 3$: the players are likely to be quite differently. Thus, the correct answer really is $P(52,5)=\binom{52}5=52\cdot51\cdot50\cdot49\cdot48\;.$

Your answer would be correct if one could ignore the order in which the cards are dealt and distinguish hands only according to which cards they contain and which one is hidden.

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    Crappy question. They don't mention anything in the book about the betting occurring between each round of dealing an up card. I agree with you that in that case order of the 4 up cards matters, but without that piece of information I would argue that my answer is the correct one. Thanks for the added info and revision!2012-03-13