How many ways can you arrange a deck of cards?

Well, the answer is complex. Let’s start with a standard deck of 52 cards.

This 52 stack of cards has been in use by millions of people worldwide for quite a few centuries; some say even an entire millennia. Millions of exact 52-card decks are shuffled each day in casinos, homes, game rooms and other venues, real or online, around the world.

The order of each deck of cards is rearranged each and every single time. However, each time you pick up a few cards from a shuffled deck of cards, you are holding an arrangement of cards that is entirely different than any other arrangement of cards in HISTORY!

How can this be possible? The answer lies in how many different arrangements of cards (or any other object) are actually possible.

52 cards may not seem like a lot, but for demonstration sake – let’s start our explanation with a smaller number – 4. Let’s say that we have 4 cards which we are required to arrange in every possible way.

In order to calculate the number of possible arrangements, we calculate the number 4 and multiply it by consecutive smaller numbers (4X3X2X1), which equals the number 24. This kind of calculation is called by mathematicians as a Factorial, which is marked by an exclamation mark – !

Just as there are 4! Factorial ways to arrange a 4-card “deck”, there are 52! Factorial ways to arrange a 52-deck of cards. We can calculate (with a calculator) the factorial number of 52 with a simple click – the number of possible arrangements for a 52-card deck is astounding – 8.065817517e+67 – this means that the latter number is comprised of 8 and 67 zeros following it. That’s a large number, a really large number.

There are more possible ways to arrange a simple deck of cards than there are ATOMS ON EARTH! The next time you’re asked to shuffle, take a moment to think about the mind-boggling mathematics involved and the mere fact that you are probably holding an arrangement of cards that has never existed and will probably never exist again!