Card maths: why a shuffled deck is a new order

Jamie captioned this clip "This amazing math fact will melt your brain". He sits at a table with a mug and a deck of cards and talks to the camera. Word captions show what he says.

He opens with a claim. He has shuffled the deck into an order "that has never existed before", and that probably never will again (frames 0:11 to 0:18). "How can I" be sure, he asks at 0:19. His answer is "it's simple maths" (0:21).

Then he explains it card by card. For the first card, "there's 52 options" (0:26). He holds up a single card at 0:26 and 0:27. The next card "could be 51 options", then 50, and so on "all the way down to number one" (0:32 to 0:34). The captions call this "a 52 vectorial", which is the factorial of 52.

At 0:40 to 0:42 the captions give the size: an 8 "followed by 68 other digits". He says that there are more orders of a deck "than there are grains of sand on the planet" (0:49 to 0:51). He fans the shuffled deck again at the close.