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.
Feel free to send any ideas and comments !

# 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 formula Show 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:
$P_{n} = n!$
where:
• $P_{n}$ - number of permutations without repetition of the n-element sequence,
• $n$ - 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:
$P_{n} = n!$
where:
• $\overline{P}_{n}^{n1,n2,\dots,n_k}$ - number of permutations with repetition of the n-element sequence,
• $n$ - number of items in the pool (it may be for example number of alphabet letters, which we use to create words),
• $n_1$ - frequency of appearance of the first element,
• $n_2$ - frequency of appearance of the second element,
• $n_k$ - 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.