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?
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I think your problem is grasping how things that are physically small can yield extremely large numbers. There is some intuition thinkable that any concept of size has to be constrained to some extend by its physical size.
What you have to intuit is that permutation grow extremely fast and that many things in nature that are large are not large due to permutations but rather sheer numbers.
There are not many obvious things in nature that are large due to the effects of permutations and so you are not used to things scaling up like that. A notable example where it does happen is entropy. The fact that for example gasses diffuse through a room is not itself a law of nature. Its pure statistics and in fact the probabilities are so enormous that diffusion MUST happen almost by statistical exclusion.
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