There are 52 cards in a poker deck.
So if you place them all face down on top of each other, there are 52 possible cards that can be first (on top of the pile).
Whatever the first one, there will be 51 possible cards that could be the second, and 50 that could be the third, 49 that could be the fourth, etc...
If the first card is the Ace of Hearts, you will have 51 possible cards that could be the second, and then you will have 50 possible cards that could be the third for each possible card that could be the second, that is, 51*50. But then you would have 49 possible cards that could be the fourth for each card that could be the third (51*50), so you would have 51*50*49 possible cards to be the fourth.
Taking this into account… Do you know how many ways to arrange a poker deck there are?
The answer is: 52! (Fifty-two factorial)
52! = 8.0659 * 10^67
That number is equivalent to 80,659,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 possible ways to arrange a poker deck.
It is estimated that the universe has existed 10,000,000,000,000,000 seconds (10^16).
So if for every second that the universe has existed you had a deck arranged differently from the rest of the decks you already have, you would only have around 7*10^51 ways to arrange a poker deck, which is equal to 7,065 .900,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 card combinations remaining.
It is such a large number that even if humanity survived until the universe ends (if we live in a finite universe), we could be shuffling new combinations every second and we would still not be able to have our deck ever sorted in all the existing ways. .
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