Combinations generator
Calculator generates list of possible combinations (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
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 combinations-
Number of results formulaShow source-
Generated results
Generation algorithm
Combinations

Some facts

  • Combination consists in choosing any number of elements from the pool but without building a new sequence. We simple pull out selected items from the pool and... its all.
  • In the case of the combination the order of the elements does not matter. It is only important if the given element is in use or not (e.g. whether a given number was drawn in the lottery).
  • If we have the n-element set and we choose k elements, then the number of possible combinations is:
    Cnk=(nk)=n!k!(nk)!C_{n}^{k} = \binom{n}{k} = \frac{n!}{k! (n - k)!}
    or if we assume that the same element can be used more than once:
    Cnk=(k+n1)!k!(n1)!\overline{C}_{n}^{k} = \frac{(k + n - 1)!}{k! (n - 1)!}
  • ⓘ 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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