Card shuffling

 

Card games and probability are two concepts that go hand in hand

 

What is the probability that a deck of cards will end up in a specific order after they are shuffled?

 

To obtain the answer, consider a standard deck of 52 cards and how many choices you have for each position in the deck.

For the first card there are 52 choices (all the cards). Then for the second card, there are 51 choices for each of the 52 choices for the first card (the deck minus the one we know comes first). We then have 50 choices for third and so on.

This produces the solution:

 

52 x 51 x 50 x 49 x ... x 2 x 1

=8.0658175 x 10^67

And thus the probability of the deck being in a specific order is roughly 1 / (8 x10^67).

This number is so astronomically large that every time you randomly shuffle a deck of card it will be the first time in history that there has been a deck of cards in that order!