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

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One deck. Fiftytwo 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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 Educator Yannay Khaikin
 Animator Nadav Arbel
 Artist Nadav Gazit
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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 (http://en.wikipedia.org/wiki/Permutation).To learn
more about how to further apply permutations and calculating probabilities, take
a look here. Anagrams: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 355thousand billion
ways. One of these arrangements spells “I am Lord Voldemort.”History: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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About TEDEd Originals
TEDEd Original lessons feature the words and ideas of educators brought to life by professional animators. Are you an educator or animator interested in creating a TEDEd original? Nominate yourself here »
Meet The Creators
 Educator Yannay Khaikin
 Animator Nadav Arbel
 Artist Nadav Gazit