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Multiset permutation / anagram count calculator

Count distinct permutations when some items repeat. Use text mode for anagrams (BANANA) or counts mode for grouped items.

Runs locally in your browser. Exact uses BigInt within safe limits; Approx shows digit count and scientific notation when the exact integer is too large.

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How to use (3 steps)

  1. Select Text (anagrams) or Counts (symbol + count).
  2. Choose Exact or Approx. Exact shows the full integer when safe.
  3. Copy a shareable URL to reproduce the same state.
Input mode

For word-level permutations (e.g., “Red, Red, Blue”), use Counts mode.

Text options

ASCII punctuation includes: !"#$%&'()*+,-./:;<=>?@[\]^_`{|}~

Precision

Results

Exact value (Exact mode):
Digits:
Scientific notation:

Breakdown (counts)

Symbol Count

Random examples (small n)

Generates distinct permutations uniformly when n ≤ 30. Use a seed for reproducibility.

    How to use this calculator effectively

    This guide helps you use Multiset permutation / anagram count calculator in a repeatable way: set a baseline, change one variable at a time, and interpret the output with clear assumptions before sharing or exporting results.

    How it works

    The calculator takes your input values, applies a deterministic formula set, and returns output using display rounding only at the final step. This means the tool is best used as a comparison engine: keep one scenario as a reference, then test alternate assumptions so you can quantify how sensitive the final answer is to each input.

    When to use

    Use this page when you need a fast planning estimate, a classroom sanity check, or a shareable scenario that another person can reproduce from the same parameters. It is especially useful before deeper modeling, because it exposes direction and magnitude quickly without requiring sign-in or setup friction.

    Common mistakes to avoid

    Interpretation and worked example

    Run a baseline case first and keep a copy of that output. Next, change one assumption to represent your realistic alternative, then compare the delta in both absolute and percentage terms. If the direction matches your domain intuition and the size of change is plausible, your setup is likely coherent. If not, review units, sign conventions, and hidden defaults before drawing conclusions.

    See also

    FAQ

    What is a multiset permutation (anagram count)?

    It counts distinct arrangements when some items are identical, e.g., the number of unique anagrams of BANANA.

    What is the formula?

    If total items are n and repeated counts are n1..nk, then Count = n! / (n1! n2! … nk!).

    What is the difference from “permutations with repetition” (n^r)?

    Multiset permutations mean the duplicates are already present (BANANA). n^r means you can reuse items while choosing (PIN codes).

    Why is the result 1 when n = 0?

    There is exactly one way to arrange zero items: do nothing (the empty permutation).

    What if Exact is rejected?

    Switch to Approx to see a reliable digit count and scientific notation without building the huge integer.

    How can I compute this in Excel?

    Use factorials: =FACT(n)/PRODUCT(FACT(n1),FACT(n2),...). For large n, Excel may overflow; use Approx here instead.

    How it’s calculated

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