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
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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
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
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
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
Note - number of permutations from m