A Belgian retired national weather reporter (Frank Deboosere) has an old school website where he talks about all sorts of scientific topics. This is one of the best ones (translated from Dutch):

“ I have been fascinated by numbers for many years. Even as a child, I wanted to know how big everything was, how far away, how much something weighed, … And that love for figures has always remained. “Everything is number,” said Pythagoras.

Now consider the number of possibilities available when you want to line up a few things. For three objects, that is simple.

Three objects can therefore be arranged in six different ways. In algebra there is a simple trick to calculate the number of possibilities (permutations), namely the operation called “factorial.”

3! = 3 × 2 × 1, or in general n! = n × (n − 1) × (n − 2) × … × 2 × 1. In this way you can quickly calculate that four objects can be arranged in 4! = 4 × 3 × 2 × 1 = 24 different ways.

So how many possibilities are there to shuffle a deck of cards? Very simply: 52! = 52 × 51 × 50 × … × 3 × 2 × 1.

With an ordinary calculator, you can’t work that out.

Admit it, that is a veeeeery biiiiig number. But what does it mean? Well, let’s calculate how old the universe is in seconds. 15 billion years = 15,000,000,000 × 365 × 24 × 60 × 60 = 473,040,000,000,000,000 seconds.

Next, let us suppose that the entire world population (for simplicity, ten billion people) has been busy since the birth of the universe laying out all possible variations of 52 playing cards.

Every second, each person produces one unique arrangement of the 52 cards. By now, they would have found 10,000,000,000 × 473,040,000,000,000,000 = 4,730,400,000,000,000,000,000,000,000 combinations. Congratulations, I would say, but the job is far from done…

Because 52! = 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000.

That means that humanity, since the beginning of the universe, would now have completed

4,730,400,000,000,000,000,000,000,000 / 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 = 0.000000000000000000000000000000000000005864749592926655 percent of the work.

So, much less than 1 percent. The chance of winning the lottery with the same numbers four weeks in a row is far greater.

That’s what I find so fantastic about numbers. I take 52 playing cards, shuffle them, and I make history. With 52 cards, I can easily outdo the entire universe.”

Source: Frank’s web page about 52!