# Permutation / Combination / Subset Generator (With Repeats) Deduplicated, lexicographic permutations / combinations / subsets of up to 12 items with exact multiset counts; display capped at 200 entries. > Canonical page: https://elysiatools.com/en/tools/combinatorial-generation - **Category:** Math & Numbers - **Keywords:** permutations, combinations, subsets, power set, multiset, repeated elements, combinatorics, next permutation, factorial, discrete math ## Overview The Permutation, Combination, and Subset Generator calculates and enumerates unique lexicographic arrangements, selections, and sub-multisets for up to 12 items. It automatically deduplicates inputs containing repeated elements and provides exact mathematical counts alongside up to 200 generated entries. ## Inputs - **Generation mode** (select) - **Items (may repeat)** (text): 1–12 items separated by commas or spaces; duplicates like 'A, A, B' are supported and only distinct results are generated. - **Size k (combinations only)** (number): How many items each combination holds; ignored in the permutations and subsets modes. - **Decimal Places** (number) ## When to use - You need to list every unique anagram or ordering from a set of characters or words containing duplicate elements. - You want to find all distinct combinations of size k chosen from an inventory with repeated item types. - You are exploring discrete math or power set problems and need to enumerate all unique sub-multisets including the empty set. ## How it works - Enter between 1 and 12 items separated by commas or spaces, including duplicates if applicable. - Select a generation mode: Permutations (all distinct full-length orderings), Combinations (distinct selections of size k), or Subsets (the full power set). - Specify the selection size k if running in combinations mode. - View the calculated multiset formula, exact total count, and the lexicographically ordered list of results capped at 200 entries. ## Use cases - Discrete mathematics students verifying multiset permutation and combination formulas against enumerated sets. - Game designers calculating distinct hand configurations or dice outcome orderings with repeated symbols. - Software developers testing algorithmic test cases requiring deduplicated lexicographic permutations. ## Frequently asked questions ### How does the tool handle repeated elements? It treats repeated elements as a multiset, using deduplication algorithms to ensure each permutation, combination, or subset appears only once. ### What is the maximum input size? The generator accepts up to 12 items per run. ### Why is the displayed output limited to 200 entries? The display is capped at 200 rows to maintain browser performance, but the calculated count always reflects the exact mathematical total. ### When is parameter k used? Parameter k is required only for Combinations mode to define how many items to choose per group; it is ignored in Permutations and Subsets modes. ### Does subset generation include the empty set? 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