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
It’s about the same as the number of atoms in the entire Milky Way.
If you go up to 58-60 cards you get the number of atoms in the observable universe.
The number of atoms on Earth is astronomically huge; around 10^(50). That is an awful lot of atoms.
The number of ways to shuffle a deck of 52 cards is 52! or about 10^(68).
There isn’t really a trick to this, or a way to explain it other than to say that factorials (which tell us how many ways we can order something) get really big really quickly.
Each time you add a card you’re taking the current number of ways to shuffle it and *multiplying* that by the number of cards you have now, because the new card can go in any place in any of the existing orders.
And that is a lot of options.
You need about 48 cards to get more than the number of atoms on the Earth.
No trick. No weird things about how atoms work or the space between them. Just a counter-intuitive result because we’re not good at thinking about numbers this big.
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