Permutations-Constanza Aceves

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Algebra I

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Permutations-Constanza Aceves

n! (n factorial)If you have 3 seats and 9 people, the first seat can be taken by 9 people, the second one by 8, and so on (9x8x7...)


A permutation is an ordered combination.

2 TYPESWith repetition: You have n choices each time.n x n x n... (r times)Without repetition:The amount of choices is reduced each time.n!/(n-r)!

They are mostly read as the possible arrangments of 'r' objects from 'n' objects.


Why are they usefulIn our everyday life permutations have multiple uses:1. To count how many combinations are possible to open a lock2. To know how many possible arrangements exist in a group of people and a number of position3. To assign phone numbers, IP adresses, and car plate numbers.

Constanza AcevesMin Jeong WooJunbai ParkRenata RodríguezP3

In phone numbers order matters because if you call 21345678 and 21345687 you will reach completely two different people.

Example of permutation trees

Examples of correctly solved permutation problems


In conclusion, permutations are useful in our life because they allow us to efficiently find the number of possible arrangements we can make. It is especially useful because it enables us to create unique codes that will not repeat themselves, such as phone numbers and car plate numbers. Not to mention that they make the life of a programmer much easier, reducing the number of operations one has to make with its amazing formula: (n!)/(n-r)!




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