How many different ways can you
put a pack of cards in order?

You can arrange these 13 cards
in over 6 billion ways!

This demonstration is taken from the book DO YOU FEEL LUCKY?

The way the numbers arrive is that for one card it's 1. For two cards it's 2x1=2 and for three cards it's 3x2x1=6. The quick way to write 3x2x1 is 3! The ! sign is called a factorial. Some calculators (including the one found on computers) have a special ! button.

Let's move on a bit.

Get ready for the BIG numbers!

If you’re good at odds and card games, you might do well at poker – have a look at this guide from to find some online sites for UK players. Or, for an easier way of putting your knowledge of odds and chance to the test, try some online casino games like roulette or blackjack – you can find the best options at this UK site. UK players looking for an alternative to playing poker online may like to try their luck playing at online casinos for UK players who offer slots, blackjack and similar games. Players from other countries where games of chance are popular like Canada may like to visit this Canadian players guide instead.

So how many ways can you order all the 52 cards in a pack?

The sum is 52x51x50x49x48....x4x3x2x1 and the answer is:

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

That's roughly the same as an 8 with 67 zeros after it.

To put this in perspective, the dinosaurs died out 65,000,000 years ago, and the age of the earth is just 4,500,000,000 years. Now suppose everybody in the world was to arrange packs of cards at the rate of one per second, it would take 600,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years to get all the combinations! That's why you're VERY unlikely ever to shuffle a pack of cards the same way twice.

There are more card facts and big numbers at Chances of Card Hands

More game numbers and stats at The Roulette Wheel - and How to Worry the Casino!

Murderous Maths Main Index Page