N-tuples and k-permutation of n generator
Calculator generates list of possible variations (with our without repetition) based on entered pool of items.

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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
Desired results length
The elements can be used more than once

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 variations-
Number of results formulaShow source-
Generated results
Generation algorithm
Variations

Some facts

  • Variation consists in choosing any number of elements from the pool and then building a new sequence from them.
  • Sequence length after variation can be different than a source sequence. Depending on whether the element can be used again or not, it can be longer, shorter or the same as the length of the original one.
  • If the number of elements in the pool is n, and we choose k elements, the number of possible variations is:
    Vnk=n!(nk)!V_{n}^{k} = \frac{n!}{(n - k)!}
    or if we assume that the same element (e.g. the letter of the alphabet) we can use more than once:
    Vnk=nk\overline{V}_{n}^{k} = n ^ {k}
  • Variation with repetition is also called n-tuples.
  • Variation without repetition is also called k-permutation of n.
  • ⓘ 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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