Believe it, or not, every time you shuffle a pack of cards you create something that no one else in the history of our planet has EVER created!
We can deduce this because counting such arrangements is very simple. Arranging three different items in a line can be done in 3×2×1 ways. Arranging eight different tiems in a line can be done in 8×7×6×5×4×3×2×1 ways, etc. Mathematicians use this pattern so often that we have created a name and a symbol for it. 8×7×6×5×4×3×2×1 is written as 8! and we call it "eight factorial." You probably have a button on your calculator labelled with [x!] that will perform these calculations for you.
When you shuffle a pack of cards, you will be creating just one out of 52! possible combinations. In this video I try to help you understand what an incredibly huge number that is! It looks deceptively small when written as 52!, but it can also be written in scientific notation as 8.065817517 × 10^67. If I attempt to write it using normal numerals, it would look like this:
It is difficult to understand or grasp the nature of a number that large (but I try). I hope you enjoy learning about the art of counting arrangements, about factorial notation, and about the amazing insights that we can gain into some of the simple acts we perform ... such as shuffling a deck of cards. Remember this next time you play!
[I apologise that (during the video), when writing the huge numeral above, I inadvertently wrote part of it off the bottom of the screen. I also made one (slightly) incorrect calculation, which I point out during the video ... but I decided to leave the video in its raw state. You will probably discern why.]