How many arrangements are there for a deck of cards

Asked 8 years, 4 months ago. Active 8 years, 3 months ago. Viewed times. Community Bot 1. Add a comment. Active Oldest Votes. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. No one has or likely ever will hold the exact same arrangement of 52 cards as you did during that game. It seems unbelievable, but there are somewhere in the range of 8x10 67 ways to sort a deck of cards. This is the nature of probabilities with such great numbers.

Though a long-time blackjack dealer might feel like they have shuffled thousands of cards in their lifetime, against a number this big, their rearrangements are irrelevant. There are simply too many ways to arrange 52 cards for any randomly organized set of cards to have repeated itself. Image by Cassandra Lee. As you deal out the deck, each subsequent position in the row has one fewer card to select from.

So the first spot has four options, the next spot has three, and so on until one card remains. This mathematical pattern can be used to calculate how many ways a set of things can be organized by multiplying these numbers together. This literally exciting calculation is denoted by an exclamation mark and is called a factorial. Further application in math and stats: In math, to permute a set of objects is another way of saying to rearrange the objects. When you pick up a deck of cards, you are holding a deck that is arranged in just one way out of many possible arrangements.

Just how many, exactly, is determined by calculating the factorial of the number of objects n! This principle of permutation can be applied when calculating probabilities and is widely used in statistics, especially in probability theory.

To learn more about how to further apply permutations and calculating probabilities, take a look here. It is believed that Shakespeare played with this idea when naming the protagonist in his play Hamlet. Another famous anagram comes from J. These 17 letters can be rearranged approximately thousand billion ways. Nevertheless, n! To learn more about the history of factorials, take a look here. Share: facebook twitter reddit whatsapp email classroom.