Card Based Questions

I was reading a poker magazine that threw up the following questions, so thought Id send them here for answers.

1. How many different 5 card poker hands [different arrangements of 5 cards] can be dealt from a standard 52 card deck?

2. If you took a 52 card deck for each different hand and piled them on top of each other, how far would they reach?

Not a poker player, so I have to ask: Do you consider Ah Kh Qh Jh 2c a different poker hand from Ah Kh Qh Jh 2s or not? Similarly, are all the possible variants of AAAxx different poker hands?

Good Point. I will modify it to state different arrangements of 5 cards, as I think for the purposes of the question they should be classed as different.

Guess I'm still not clear on the question. Are you now just asking for Comb(52,5)=2,598,960 or Perm(52,5)=311,875,200 ? Probably something else, but I'm just not following yet.

To be honest, Im not sure myself but I am thinking that the second answer you gave is the one we may be looking for, as I think I remember the magazine mentioning something about 2,598,960 hands. Maybe you could help me clean up the question to more appropriately apply.

Well, it that is the answer you want to get to, I would have said, "How many different combinations of five cards could be selected from a 52-card deck?" My handiest deck of cards is 9/16" thick, so I estimate that number of decks as totaling a little over 23 miles thick.

Reminds me of the problem I mentioned not too long ago about theoretically doubling over a piece of paper far too many times.