All of us know that there are 52 cards in a deck. But what if you wanted to get the exact same order of cards that you started with after shuffling? Well, let’s just say you’ll have to sit and shuffle past the end of the universe!
The chances of getting the same sequence of cards back again is infinitesimally small, it’s almost impossible. This is because the total number of ways in which you can arrange a deck of cards is 52!. This equals 8x10^68 (meaning 8 followed by 68 zeroes). Now that is a huge, huge number!
Let’s consider only 3 cards to understand this.
In order to arrange these cards, to fill the first place you have 3 cards. Now for the second place you are left with 2 cards, so you can fill the second place in 2 ways. And for the last place you have only 1 card left.
So the total number of ways in which you can arrange is 3x2x1 = 6.
Similarly, for obtaining the number of ways in which you can arrange 52 cards, you’ll have to perform this calculation:
52x51x50x49………….…x3x2x1 and this gives the number 8x10^68.
This is a very, very huge number. It’s even larger than the total number of stars in the sky. It’s actually very close to the total number of atoms in our galaxy!
So if you were to obtain all the possible combinations, you would take approximately 23 quindecillion years (23 followed by 48 zeros)!!! Assuming you’d started shuffling since the Big Bang, even by today there’s no way you could’ve got all the combinations!
Here's a lil tip: Next time you shuffle a deck of cards, feel extremely special because you’d be holding something that is very unique!