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
The earths mass is approximately 6×10^24 kg. The average atomic mass is 40u, or 6.64×10^-26 kg. So the rough number of atoms on the earth is 9×10^50 atoms.
That part is pretty straightforward.
How many combinations are there in a deck of cards? The answer is 52! (The exclamation point standing for factorial, not like wow 52!)
52! = 52×51×50×…×3×2×1 = 8×10^67
Why so many? Well think about it. How many ways are there to arrange the deck when you keep the order of every card the same except you exchange the top one for a different card? 52 right? Now do that again except now you can exchange the top two cards for any other 2. The number of combinations there is 52×51. Its one less because the original 52 combinations already contained one of the orders that would occur when moving the second card as well. Keep going like this and the pattern continues. Allowing for the top 3 cards to be exchanged while keeping the rest in order would lead to 52×51×50. And so on like that. So the total number of combinations would be 52!
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