# How many possible arrangements are there for a deck of 52 playing cards?

1. Feb 9, 2004

### jlmac2001

How many possible arrangements are there for a deck of 52 playing cards? ( For simplicity, consider only the order of the cards, not whether they are turned upside down)

Answer: Since there are 52 cards, each card has 52 possiblilites so 52*52=2,704. is this right?

Suppose you start with a sorted deck and shuffle it repeatly, so that all arrangements become accessible. How much entropy do you create in the process? Express answer as pure number (neglecting the factor k) and the SI units.

Stotal=k ln omega(total)= ln(2,704)=7.902
7.902 is the amount of entropy created.

Is this entropy significat compared to the entropy associated with arranging thermal energy among the molecules in the cards?

answer: I don't know?

2. Feb 9, 2004

### curiousbystander

Not knowing much about entropy I can't answer your complete question, but I can say that there are 52! (that's 52*51*50*49*....* 3*2*1) distinct permutations of your cards (assuming no trickery with orientation) not 52*52:
You can see it pretty easily with 4 items (I'd do three but that's a little too trivial):
1234_2134_3124_4123
1243_2143_3142_4132
1324_2314_3214_4213
1342_2341_3241_4231
1423_2413_3412_4312
1432_2431_3421_4321

Notice how there are 4 cols? And in each column there are 3! ways of arranging the last three numbers? That's where the 4*3*2*1 comes from.