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
Lets do an estimation. If we know the Earth’s volume Ve and the volume of an atom Va we can estimate how many of them are roughly in Earth by Ve/Va. Ve = ~ 10²¹ m³ and Va= ~ 4/6 (10^(-10))³ pi this gives us for Ve/Va = ~ 4.77 × 10⁵⁰ number of atoms.
How many ways can 52 different cards can be arranged. Well you have 52 options for the first card, 51 for the second 50 for the third and so on. We multiply the number of possibilities for each card in the deck since any card can be second except for that 1 which is first. So the total number of psooible arrangements or rather permutations is 52! = 52×51×50×49×…×3×2×1. Now 52! = ~8×10⁶⁷ possible permutations.
So the number of atoms in Earth are smaller than all possible permutations of 52 cards. Our estimated value for the number of atoms in Earth is about 42!/3. So even 42 cards can be arranged in more ways than the number of atoms.
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