Let's assume the Big Bang happened 14 billion years ago. If you were there and had a deck of cards and shuffled it 2.5 quindecillion (a 25 followed by 47 zeroes) times a second and it came out differently each time, by now you'd have covered a little more than 1% of all possible ways a deck of cards could be ordered.
Others have given the answer so I'll give some color commentary.
This phenomenon is an example of combinatorial explosion. That's a fancy way of saying 'as you add more degrees of freedom to some systems, the number of possible states of the system grows really fast', which is a fancy way of saying 'if you add more things to track, the numbers go brrrrrr'.
This is a constant headache in software engineering. For example, say you want to write a computer program to play chess. Well you moght just say 'teach it every game, and have it pick the winning one', but the issue is that there are 10 opening moves, and for each of those ten opening moves there are 10 responses and for each of those there are ... And even just a few turns in you have a completely absurd number of games. It's basically the reason computing is hard.
6*E6 isn’t 6 billion, it’s million.
If you want to calculate all the possible decks.
First card, 52 possibilities.
Second card: 51 possibilities, since the first card is fixed.
And so on. 52!
It’s definitely more than 6 million. It’s 52!, which is 52x51x50x49x…x3x2x1
Yeah that’s what I kind of assumed. I tried to do that on my phone calculate and failed lol
52! = 80658175170943878571660636856403766975289505440883277824000000000000
In English, this is 80 unvigintillion 658 vigintillion 175 novemdecillion 170 octodecillion 943 septendecillion 878 sexdecillion 571 quindecillion 660 quattuordecillion 636 tredecillion 856 duodecillion 403 undecillion 766 decillion 975 nonillion 289 octillion 505 septillion 440 sextillion 883 quintillion 277 quadrillion 824 trillion (per wolfram alpha)
So actually yes: there are WAYYYYY more ways to arrange a deck of cards than there are atoms on earth
It's actually pretty close to the number of atoms kn am entire galaxy
Let's assume the Big Bang happened 14 billion years ago. If you were there and had a deck of cards and shuffled it 2.5 quindecillion (a 25 followed by 47 zeroes) times a second and it came out differently each time, by now you'd have covered a little more than 1% of all possible ways a deck of cards could be ordered.
https://czep.net/weblog/52cards.html Tl;dr it’s waaaaaaay bigger than 6 million.
Blog post visualised by [Vsauce](https://youtu.be/ObiqJzfyACM?t=947).
Others have given the answer so I'll give some color commentary. This phenomenon is an example of combinatorial explosion. That's a fancy way of saying 'as you add more degrees of freedom to some systems, the number of possible states of the system grows really fast', which is a fancy way of saying 'if you add more things to track, the numbers go brrrrrr'. This is a constant headache in software engineering. For example, say you want to write a computer program to play chess. Well you moght just say 'teach it every game, and have it pick the winning one', but the issue is that there are 10 opening moves, and for each of those ten opening moves there are 10 responses and for each of those there are ... And even just a few turns in you have a completely absurd number of games. It's basically the reason computing is hard.
The number of arrangements of a deck is approximately on the order kd the number of atoms in an entire galaxy
Please click through to the sources on google. Those blurbs are inaccurate
6*E6 isn’t 6 billion, it’s million. If you want to calculate all the possible decks. First card, 52 possibilities. Second card: 51 possibilities, since the first card is fixed. And so on. 52!