Combinatorics – combinations, arrangements and permutations

Below is a calculator that computes the number of combinations, arrangements and permutations for given n and m. A little reminder on those is below the calculator.

Combinatorics. Combinations, arrangements and permutations

n

m

Calculate

Number of permutations from n

 

Number of arrangements of m from n

 

Number of combinations of m from n with repetitions

 

Number of combinations of m from n

 

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So, assume we have a set of n elements.

Each ordered set of n is called a permutation.

For example, we have a set of three elements – А, В and С.
An example of an ordered set (one permutation) is СВА.
The number of permutations from n is

Example: For the set of А, В and С, the number of permutations is 3! = 6. Permutations: АВС, АСВ, ВАС, ВСА, САВ, СВА

If we choose m elements from n in a certain order, it is an arrangement.

For example, the arrangement of 2 from 3 is АВ, and ВА is the other arrangement. The number of arrangements of m from n is

Example: For the set of А, В and С, the number of arrangements of 2 from 3 is 3!/1! = 6.
Arrangements: АВ, ВА, АС, СА, ВС, СВ

If we choose m elements from n without any order, it is a combination.

For example, the combination of 2 from 3 is АВ. The number of combinations of m from n is

Example: For the set of А, В and С, the number of combinations of 2 from 3 is 3!/(2!*1!) = 3.
Combinations: АВ, АС, СВ

Here is the dependency between permutations, combinations and arrangements

Note – the number of permutations from m