Permutation & Combination (nPr, nCr)
Calculate exact permutations and combinations with BigInt for n up to 10000. See every result digit and the complete factorial expansion.
About this permutation & combination (npr, ncr)
Calculate exact permutations and combinations with BigInt for n up to 10000. See every result digit and the complete factorial expansion Computes exact algebraic and numerical metrics directly in your browser using IEEE 754 precision without round-trip latency.
Formula & calculation mechanics
The execution engine processes input tokens and applies transformations in the browser sandbox. Specifically, Choose r distinct elements from n distinct elements without replacement. P(n,r)=n!/(n−r)! counts ordered selections; C(n,r)=n!/[r!(n−r)!] counts unordered selections. 0!=1, and selecting zero elements gives 1 in both cases. This calculator counts selections; it does not list them.
Worked numerical calculation
Scenario: What should the example produce?
Sample input:
Processing: Enter total n and selection size r. Calculate the ordered and unordered counts. Open each expansion to inspect the factorial cancellation.
Illustrative output:
Domain range & precision boundaries
Integers 0 ≤ r ≤ n ≤ 10000; each input at most 32 UTF-16 code units including whitespace. Native BigInt arithmetic preserves every result digit. Combination calculation uses k=min(r,n−r) and alternating multiplication and exact division, avoiding full factorials. The limit bounds browser work; it is not a file or usage quota. Results are complete decimal integers, without rounding or scientific notation. Scroll inside the result and expansion fields to inspect or select all text. Local browser calculation with no added calculation dependency, fee or external service. Works offline after loading.
Calculations in Permutation & Combination (nPr, nCr) use standard IEEE 754 precision or exact rational models. Verify significant accounting or tax figures with authoritative references.
In-browser calculation boundary
Formula calculations and numeric evaluations in Permutation & Combination (nPr, nCr) run synchronously in the browser JavaScript engine with zero server telemetry.
Mathematical formulas & precision standards
Mathematical constants, IEEE 754 floating-point standards, and numerical analysis specifications:
- NIST Digital Library of Mathematical Functions, §1.2 — Elementary Algebra
- ECMAScript 2026, §6.1.6.1 Number Type
Permutation & Combination (nPr, nCr) verification · Audit standards
How to use it
- Enter, paste, or select your input data into the Permutation & Combination (nPr, nCr) workspace controls.
- Review parameter fields, units, or options configured for Permutation & Combination (nPr, nCr).
- Click the action button or observe immediate live calculations rendered by Permutation & Combination (nPr, nCr).
Frequently asked questions
What do these counts mean?+
Choose r distinct elements from n distinct elements without replacement. P(n,r)=n!/(n−r)!
How are huge results kept exact?+
Use C(n,r)=C(n,k), k=min(r,n−r). Cancel (n−k)!; the expansion lists every numerator factor and every factor of k!. An empty product is 1.
What limits and display rules apply?+
Runtime handling of "What limits and display rules apply?" executes synchronously in your browser tab without remote delays.
What should the example produce?+
Security isolation for "What should the example produce?" ensures zero transmission beyond your local workstation.