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
Ever hear about how if you double a penny every day you get $1 million dollars after a month? It’s kind of like that in that the numbers get large quickly in a way that’s not intuitive.
If you have only five cards how many possibilities are there?
5 * 4 * 3 * 2 * 1 = 120. Seems reasonable.
If you have 10 cards how many possibilities are there?
10* 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800!
You doubled the number of cards but the number of possibilities grew incredibly larger! This is the nature of “factorials”
How about 20 cards?
20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 2.432902×10^18 which is:
2,432,902,000,000,000,000
And that’s barely half of a deck of cards! Let’s add six cards to make it half:
26! (26 factorial which is how we notate the above math) = 4.0329146×10^26
403,291,460,000,000,000,000,000,000
The difference between half a deck and a full deck?
52! is 8.0658175×10^67
or:
80,658,175,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Edit: Fixed some errors because math is hard.
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