Permutations generator
This calculator generates list of possible permutations (with or without repetition) based on entered pool of items.

Beta version

BETA TEST VERSION OF THIS ITEM
This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
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Pool of items and desired type of results

Detected pool of items

Generated results

Pool of items
Detected pool of items
Elements frequency of appearance in the pool
Total number of items in the pool
Number of unique items in the pool
Number of results
Number of possible permutations-
Number of results formulaShow source-
Generated results
Generation algorithm
Permutations

Some facts

  • Permutation consists in changing the order of elements in the sequence. Colloquially, we can say that permutation is a mixing of elements.
  • The permutation result includes the same number of elements as the source set.
  • If we have a n-element set, the amount of its permutation is:
    Pn=n!P_{n} = n!
    where:
    • PnP_{n} - number of permutations without repetition of the n-element sequence,
    • nn - number of items in the pool (it may be for example number of alphabet letters, which we use to create words).
  • If some elements in original set occures more than once, then not all permutations are unique, e.g. swappning 1-st and 3-th letters in the word "eye" gives the same word. If we exclude non-unique words, then the amount of permutation is:
    Pn=n!P_{n} = n!
    where:
    • Pnn1,n2,,nk\overline{P}_{n}^{n1,n2,\dots,n_k} - number of permutations with repetition of the n-element sequence,
    • nn - number of items in the pool (it may be for example number of alphabet letters, which we use to create words),
    • n1n_1 - frequency of appearance of the first element,
    • n2n_2 - frequency of appearance of the second element,
    • nkn_k - frequency of appearance of the k-th element (e.g. the frequency of the letter "e" in the word "eye" is 2).
  • ⓘ Hint: More combinatorial items on Calculla:
    • combinatorial tables - short crib with common combinatorics related formulas,
    • permutations generator - simple tool to create list of all possible permutations (with or without repetition) based on given input pool of items,
    • combinations generator - simple tool to create list of all possible combinations (with or without repetition) based on given input pool of items,
    • variations generator - simple tool to create list of all possible variations (with or without repetition) based on given input pool of items.

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