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# Combinatorics. Combinations, arrangements and permutations

This calculator calculates number of combinations, arrangements and permutations for given n and m

Below is the calculator which computes 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

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 permutation.

For example, we have set of three elements - А, В, and С.
Example of ordered set (one permutation) is СВА.
Number of permutations from n is
$P_n = n!$

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

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

For example, arrangement of 2 from 3 is АВ, and ВА is the other arrangement. Number of arrangements of m from n is
$A_{n}^m=\frac{n!}{(n-m)!}$

Example: For set of А, В, С 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 combination.

For example combination of 2 from 3 is АВ. Number of combinations of m from n is
$C_{n}^m=\frac{n!}{m!(n-m)!}$

Example: For set of А, В, С 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
$C_{n}^m=\frac{A_{n}^m}{P_m}$
Note $P_m$ - number of permutations from m