Multiset Permutation Calculator
Count exact arrangements of a collection containing repeated indistinguishable items.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Count the total number of items. Form the factorial of that total. Divide by the factorial of each repeated-group size. Report the exact integer arrangement count.
Distinct arrangements=(Σnᵢ)!/∏nᵢ!
Worked example
Group counts 2, 2 and 1 give 5!/(2!×2!×1!)=30 distinct arrangements.
Assumptions and input details
Up to thirty groups and five hundred total items. Members of a group are indistinguishable. This is ordering an entire multiset, not sampling with replacement. The empty collection has one arrangement.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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