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Math & AlgebraGenerated accuracy model review: 2026-05-06
Permutation & Combination accuracy and testing
This page documents how Calwarden builds trust for this calculator: source notes, regression-style default tests, limitations, assumptions, unit handling, rounding, and visible change history.
Formula source
- The math relies on factorials ($n!$): * **Permutation (nPr):** $\frac{n!}{(n-r)!}$. Counts arrangements where order matters (ABC is different from CBA). * **Combination (nCr):** $\frac{n!}{r!(n-r)!}$. Counts selections where order is irrelevant (ABC is the same as CBA).
Test cases
Default input regression check
Generated from the checked-in default inputs and calculate function.
Inputs
- n (Total Items): 10
- r (Chosen Items): 3
Expected outputs
- Permutations (nPr): 720
- Combinations (nCr): 120
Known limitations
- This page documents the checked-in calculator logic and does not certify results for every real-world edge case.
- Use the result as a planning estimate unless the calculator page states a stricter purpose.
Assumptions
- Inputs should be whole numbers with 0 <= r <= n.
- This calculator assumes you are choosing from distinct items without replacement.
- Permutation counts orderings, while combination removes duplicate orderings of the same chosen set.
Unit handling
- n (Total Items) accepts numeric values.
- r (Chosen Items) accepts numeric values.
Rounding rules
- Number displays use up to 2 decimal places in the calculator UI.
Version history
1.0.0 - 2026-05-06
Generated accuracy and testing page from the current permutation-and-combination-calculator calculator definition.
Change log
2026-05-06
Published default regression test documentation and metadata fallbacks for Permutation & Combination.
Calculator transparency
Accuracy pages are generated from checked-in calculator definitions and can be upgraded with curated review metadata over time.