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Copy pathFAC.txt
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49 lines (25 loc) · 714 Bytes
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Permutations -
factorial is number of possibilities
e.g.
how many words can be made by rearranging the letters of VECTOR
6! = 6x5x4x3x2x1 = 720
trickier permutations-
how many 4 letter words can be made by rearranging GHIJKLM
7!/3! = 840
options!/(options-limit)!
because 7!/3! = 7x6x5x4 x 3!/ 3!
Combinations
if you dont care about order e.g abb is the same as bab then divide by the factorial of the limit
e.g.
7!/(7-4)!4!
if we have n objects and want to choose a group of r of them where order does not matter,
(n)
(r) = n!/r!(n-r)!
82!/80!2!
82 * 81 / 2!
Binomial Theorem
fancy way to multiple out brackets ig
(a+b)^n = n sigma r=0 (n)a^(n-r)b^r
(r)
f'(1) = 6
6*e^(6-b)