How can there be more ways to arrange a deck of cards than there are atoms on earth?

Question

I understand the math behind it, I just can’t wrap my head around the fact that something so common and limited like a deck of cards can have more ways to be arranged than something so massive like the earth with all its oceans and mountains has atoms.

In my mind it would make more sense that even a little pond has more atoms than there are deck arrangements.

Could it be due to the fact that atoms have a lot of empty space in them?

In: 318

Answer 1

Pick one card, you have 1 in 52 chance of getting the one you picked. Pick two cards, you have a 1 in 51 chance of getting the one you picked. And so on, until you go through the whole deck. Hence, there are 52*51*50*…*3*2*1 different possible permutations or 52!=~8.066*10^67. I don’t know if that’s more than the number of atoms in the universe, but it’s a pretty fucking big number as it is 67 digits long.