From 9cf7e09a0d6abdfd93d535bd2605b495a1a4e1eb Mon Sep 17 00:00:00 2001 From: TheRealSpartacus Date: Mon, 3 Dec 2018 14:48:03 -0800 Subject: [PATCH] Adding content (#23436) Saw guide was empty, filled it --- .../mathematics/permutation-formula/index.md | 37 +++++++++++++++---- 1 file changed, 30 insertions(+), 7 deletions(-) diff --git a/guide/english/mathematics/permutation-formula/index.md b/guide/english/mathematics/permutation-formula/index.md index ae35933886..a1b9ccca33 100644 --- a/guide/english/mathematics/permutation-formula/index.md +++ b/guide/english/mathematics/permutation-formula/index.md @@ -3,6 +3,35 @@ title: Permutation Formula --- ## Permutation Formula +In probability, a permutation is an ordered set of elements created from a larger set of possible elements. In order to know the number of all possible permutations of a specific size that can be made from any given set of elements, we use the permutation formula which is as follows: + +![alt text](https://github.com/TheRealSpartacus/sources/blob/master/PermForm/PermForm%20Formula.PNG "Permutation Formula") + +where *n* is the number of elements in the set of possible elements and *r* is the number of elements in the permutation of elements from the set of possible elements + +To get the total number of possible permutations of size *r* from a set of size *n*, you first take the factorial (!) of *n*. Next you'll take the difference of *r* from *n* and then take the factorial of that difference. Then you divide the first factorial by the difference factorial to get the total number of possible permutations. + +For example, if you wanted to know the total numbers of 4-digit number codes possible for a cell phone, you would first find the values for *n* and *r*. + +Since the size of the code is 4 digits and the number of different numerals is 10, *n* = 10 and *r* = 4 +Now we plug in *r* and *n* to the permutation formula: + +![alt text](https://github.com/TheRealSpartacus/sources/blob/master/PermForm/PermForm%20Fig.%201.PNG "Fig. 1") + +Next, we take the difference of *n* and *r*: + +![alt text](https://github.com/TheRealSpartacus/sources/blob/master/PermForm/PermForm%20Fig.%202.PNG "Fig. 2") + +Then, we take the factorial of both the numerator and denominator: + +![alt text](https://github.com/TheRealSpartacus/sources/blob/master/PermForm/PermForm%20Fig.%203.PNG "Fig. 3") + +Finally, we divide each result to get the total number of possible 4 digit codes for a cell phone: + +![alt text](https://github.com/TheRealSpartacus/sources/blob/master/PermForm/PermForm%20Fig.%204.PNG "Fig. 4") + +### Another Explanation + If I took a list of 3 color {red, blue, green}. How many ways could I arrange this? {red, blue, green} @@ -85,12 +114,6 @@ n!/(n-k)! So, from the example above, 4!/(4-2)! = 24/2 = 12. - #### More Information: - -Helpful Khan Adcamedy video: -https://www.khanacademy.org/math/precalculus/prob-comb/combinatorics-precalc/v/permutation-formula - - - +- [Helpful Khan Adcamedy video](https://www.khanacademy.org/math/precalculus/prob-comb/combinatorics-precalc/v/permutation-formula)