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

Numbers are just numbers. When you use exponents, you can get to very high numbers very fast. The classic example is [trying to fill a chessboard with wheat](https://en.wikipedia.org/wiki/Wheat_and_chessboard_problem). 2^x becomes too high too fast.

You need to stop thinking naively using common (non)sense and start thinking mathematically.