Shuffling a deck of cards question?

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A properly shuffled deck of 52 cards can be arranged in approximately 8*10^67 different ways, a number comparable to the total number of atoms in the universe. This immense variety makes it statistically probable that each shuffle results in a unique order that has never existed before. Given the vast number of possible combinations, the likelihood of repeating a specific order is extremely low. Therefore, every time a deck is shuffled, it is highly likely that it is in a configuration that no one has encountered previously. This highlights the fascinating complexity of card shuffling and the uniqueness of each arrangement.
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Is it statistically probable that a properly shuffled deck of cards will be in an order that has never before existed amongst other decks?
Please explain!
 
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What do you think? How do you reach whatever conclusion you reach? How many ways can a deck of cards be ordered?
 
amantonas said:
Is it statistically probable that a properly shuffled deck of cards will be in an order that has never before existed amongst other decks?
Please explain!

Yes, it is extremely likely so, if you have a deck with, let's say, 52 cards, it means that there are 52! different ways to shuffle it, that number is gigantic, around 8*10^67 which is a number close to the number of atoms in the universe.

In summary, every time you shuffle a deck properly chances are you have shuffled something no one has shuffled before... in this universe.
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...

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