Adding Permutations (#20912)

These are permutation formulas. I also added a helpful video for those who are visual learners.

guide/english/mathematics/permutation-formula/index.md

@@ -3,13 +3,94 @@ title: Permutation Formula
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 ## Permutation Formula
 
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+If I took a list of 3 color {red, blue, green}. How many ways could I arrange this?
 
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+{red, blue, green}
+{red, green, blue}
+
+{blue, red, green}
+{blue, green, red}
+
+{green, blue, red}
+{green, red, blue}
+
+In a list of 3 colors, I had 6 arrangements. 
+6 = 3! (3 X 2 X 1)
+
+In another example, I take 4 letters {m, a, l, c} and arrange them in all the possible ways.
+
+{m,a,l,c}
+{m,a,c,l}
+{m,l,c,a}
+{m,l,a,c}
+{m,c,a,l}
+{m,c,l,a}
+
+{a,m,l,c}
+{a,m,c,l}
+{a,l,c,m}
+{a,l,m,c}
+{a,c,m,l}
+{a,c,l,m}
+
+{l,m,a,c}
+{l,m,c,a}
+{l,a,c,m}
+{l,a,m,c}
+{l,c,m,a}
+{l,c,a,m}
+
+{c,m,a,l}
+{c,m,l,a}
+{c,a,l,m}
+{c,a,m,l}
+{c,l,m,a}
+{c,l,a,m}
+
+In total, that is 24 ways. 24 = 4! (4X3X2X1)
+
+See a pattern?
+
+In general, when asked how many ways can you arrange a list where order matters (meaning {1,2} != {2,1}), the formula is as follows:
+
+n!, where n is the number of elements in the list.
+
+Now, lets says we are asked how many ways arrange 2 out of the 4 letters.
+
+{m,a,l,c}
+
+{m,a}
+{a,m}
+
+{m,l}
+{l,m}
+
+{m,c}
+{c,m}
+
+{a,l}
+{l,a}
+
+{a,c}
+{c,a}
+
+{l,c}
+{c,l}
+
+That is 12 different ways.
+
+When asked how many ways to arrange k elements from a list of n elements the formula is as follows:
+
+n!/(n-k)!
+
+So, from the example above, 4!/(4-2)! = 24/2 = 12.
 
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 #### More Information:
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+Helpful Khan Adcamedy video:
+https://www.khanacademy.org/math/precalculus/prob-comb/combinatorics-precalc/v/permutation-formula
+
+