The Size of 52!

You may have heard that if you shuffle a deck of playing cards, you probably have it in an order that no one had before or ever will have it again. That is because the number of all permutations is 52! (! stands for faculty and represents a number calculated like this: 52*51*50*...*3*2*1). So how much is that?

80658175170943878571660636856403766975289505440883277824000000000000

You can see that it's large, but you still probably can't imagine the sheer size of it. So to blow your mind I will use the following comparison.

Let me start a timer that will count down the number of seconds from 52! to 0. Menwhile lets do some activities to pass the time.

Let's start at some point on the equator. I'm going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. To fill my time I have packed a deck of playing cards, so I can get in a few trillion hands of solitaire between steps. After I complete my round the world trip, I remove one drop of water from the Pacific Ocean. Now do the same thing again: I will walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time I circle the globe. The Pacific Ocean contains 707.6 million cubic kilometers of water. Let's continue until the ocean is empty. When it is, I take one sheet of paper and place it flat on the ground. Now, let me fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time I’ve emptied the ocean. I will repeat this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits haven’t even changed. I still have 8.063e⁶⁷ more seconds to go. So, I take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385e⁶⁷ seconds remaining. We’re just about a third of the way done.

To pass the remaining time, let's start shuffling the deck of cards. Every billion years I deal myself a 5-card poker hand. Each time I get a royal flush, I buy myself a lottery ticket. If that ticket wins the jackpot, I throw a grain of sand into the Grand Canyon. I keep going and when I’ve filled up the canyon with sand, I remove one ounce of rock from Mt. Everest. Now I empty the canyon and start all over again. When I’ve levelled Mt. Everest, look at the timer, I still have 5.364e67 seconds remaining. I barely made a dent. If I were to repeat this 255 times, we would still be looking at 3.024e⁶⁴ seconds. The timer would finally reach zero sometime during my 256th attempt.

Of course, in reality none of this could ever happen. The truth is, the Pacific Ocean would boil off as the Sun becomes a red giant before I could even take the fifth step in my first trek around the world. But don't let that stop you from getting the same deck twice the next time you shuffle :)

Source: https://czep.net/weblog/52cards.html