Question

A new deck of cards has all the suits (clubs,diamonds,hearts,and spades) in order, and the cards are ordered by number within the suits. If you shuffle the cards many times, are you likely to return the cards to their original order? Explain. This is an example of what physical law?

Answer 1

You are not likely at all to return them to their original order. In fact if you come across a deck of shuffled cards (or shuffle a new deck 7 times or so) you very likely have an ordering of cards that has never been achieved before (ever in history) Why? Because of the large number of ways there are to have a deck arranged it is statistically unlikely, in the extreme. The total number of ways is given by 52!, which is


`52!=52*51*50*49*...*1 =8.0658 * 10^6^7`

To give you an idea of just how big this is, it is estimated that there are about
2x10^67 atoms in the milky way galaxy. That means there are (roughly) four times as many ways to arrange a single deck of cards than there are atoms in the entire galaxy of stars, planets, gas clouds etc. If this doesn't blow your mind, I don't know what will. You are thus far more likely to win the lottery every week for the rest of your life than randomly shuffle a deck of cards a bunch of times and have any one of the configurations be the same.
This is an example of the 3rd law of thermodynamics. We are unlikely to see the same arrangement due to the fact that there are just so many to choose from.