Number of 5 card stud poker hands 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?

**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.