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How many ways can you arrange a deck of cards? - Yannay Khaikin


6,944 Questions Answered

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One deck. Fifty-two cards. How many arrangements? Let's put it this way: Any time you pick up a well shuffled deck, you are almost certainly holding an arrangement of cards that has never before existed and might not exist again. Yannay Khaikin explains how factorials allow us to pinpoint the exact (very large) number of permutations in a standard deck of cards.

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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 permutation look here (
To learn more about how to further apply permutations and calculating probabilities, take a look here.
An ANAGRAM is a kind of wordplay where the letters in a word, phrase or sentence are rearranged to make a new word, phrase or sentence. For example, the word ANAGRAM has 7 letters and can be rearranged 7! = 5040 ways. One of these arrangements spells the word ANAGRAM itself, another spells MARGANA, and so on. It is believed that Shakespeare played with this idea when naming the protagonist in his play Hamlet. Hamlet’s name is thought to have been an anagram of AMALETH, the name of a Danish Prince. Another famous anagram comes from J.K. Rowling’s book Harry Potter and the Chamber of Secrets. The name “Tom Marvolo Riddle” has 17 letters. These 17 letters can be rearranged approximately 355-thousand billion ways. One of these arrangements spells “I am Lord Voldemort.”
The first person to ever use ! to symbolize a factorial was a French mathematician named Christian Kramp. In a preface to Elements d'arithmétique universelle (in English, Universal Elements of Arithmetic), published in 1808, he writes, “I use the very simple notation n! to designate the product of numbers decreasing from n to unity, i.e. n(n - 1)(n - 2) ... 3 . 2 . 1.” It’s not clear why Kramp chose this symbol, and some mathematicians have criticized this choice claiming that it is ridiculous to use symbols found in ordinary language. Nevertheless, n! has been adopted universally. To learn more about the history of factorials, take a look here.

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Meet The Creators

  • Educator Yannay Khaikin
  • Animator Nadav Arbel
  • Artist Nadav Gazit
  • Narrator Addison Anderson

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