The number of possible permutations in the deck of cards is about 8 × 1067

Playing cards in its current 52-card form has been known for more than five hundred years. Let's assume (although this is not true), that the current world population (about six billion people) - remained unchanged during these five centuries. Applying a little math, we get a number in the nine trillion person-years in the fictitious example. Or, to make this number even more - about 9 × 1019 person-seconds. It is nine and 19 zeros.

If every living person in the course of these five hundred years, shuffling a deck of cards at a rate of one deck to the second, we would have the number of shuffled decks during this time. This is a large number - 90, 000, 000, 000, 000, 000, 000

And almost certainly you can say that each of these shuffled deck would be unique.

The number of possible permutations in the deck of cards is 52! (52 factorial), or approximately 8 × 1067 This is such a big number, it does not even fit on the line, so we will divide it into two parts: 8, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000,
000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000.

Now we got a really huge number. How great? It is literally beyond the scope of the astronomical - According to the calculations of the Australian team of astronomers, the number of stars in the foreseeable part of the galaxy is only 7 × 1022

To get at least 50% chance to repeat reshuffle, a person must make a 9 × 1033 shuffles. And all of humanity, as we could make only 9 × 1019. In other words, each time you shuffle a deck of cards, you will almost certainly create a combination that the universe has not seen.

via factroom.ru