Permutation & Combination
Compute nPr and nCr quickly with clear definitions. Free MyCalcsWorld statistics/math tool with FAQ and worked example.
Results
P(10,3)
C(10,3)
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Educational estimates · not financial advice · free, no signup
Formula / how it works
Outputs follow the usual algebraic / geometric / statistical identities for this tool. Intermediate rounding is limited; final display uses sensible fixed precision so classroom checks stay reproducible. For proofs or contest math, re-derive with the exact symbolic form your course requires. For the Permutation & Combination, the labeled fields (n, r) drive the live result panel.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
The Permutation & Combination on MyCalcsWorld keeps inputs labeled and formula notes visible so you can reconcile with a textbook or homework key. What it does: Compute P(n,r) and C(n,r) for counting problems. Typical inputs: n, r. Demo defaults (n 10, r 3) currently resolve to P(10,3) 720; C(10,3) 120 in the live panel — change any field to explore sensitivity. Who it helps: students, tutors, contest-prep learners, and professionals who need a transparent check against homework or hand math.
When to use / who it helps
- Homework checks for counting problems.
- Interview or contest prep warm-ups.
- Explaining order-matters vs order-does-not to a student.
- Use the Permutation & Combination to check homework, contest practice, or a quick engineering sketch.
- Mirror the same numbers on paper using the formula notes when exams ban calculators.
How to use
Steps
- Enter n (total items).
- Enter r (chosen items).
- Read permutation and/or combination outputs.
- Match the definition to your word problem.
- Open the Permutation & Combination on MyCalcsWorld and skim the labeled fields before you type.
- Set n — demo default is 10.
How to interpret results
- nPr = n! / (n−r)! — order matters.
- nCr = n! / (r!(n−r)!) — order does not.
- Large n may hit floating-point limits.
- Each result is driven only by the labeled inputs (n, r); anything not on the form (fees, holidays, clinical adjustments) is outside this estimate.
- Read the primary result first, then any secondary roots, steps, or geometric properties the panel lists.
Common mistakes & gotchas
- Using nCr when ranks mean order matters (nPr).
- Entering r > n.
- Forgetting identical items need different formulas.
- Mixing degrees and radians, or skipping parentheses, when the Permutation & Combination assumes a specific convention.
- Comparing rounded display values to an answer key that wants exact fractions.
Worked example
Worked example — n=10, r=3
- n = 10, r = 3.
- nPr = 10×9×8 = 720.
- nCr = 720 / 3! = 120.
- Open the Permutation & Combination (permutation combination) and note the starting defaults (n 10, r 3).
Result: With defaults (n 10, r 3), the Permutation & Combination shows: P(10,3) 720; C(10,3) 120.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
Outputs follow the usual algebraic / geometric / statistical identities for this tool. Intermediate rounding is limited; final display uses sensible fixed precision so classroom checks stay reproducible. For proofs or contest math, re-derive with the exact symbolic form your course requires. For the Permutation & Combination, the labeled fields (n, r) drive the live result panel.
Frequently asked questions
When do I use permutation vs combination?
If rearranging creates a new outcome, use permutations. If only the set matters, use combinations.
Does this handle repetition?
Classical nPr/nCr assume without repetition. With-repetition formulas differ.
What if r = 0?
C(n,0)=1 and P(n,0)=1 by convention for non-negative n.
Why did I get an error for large n?
Factorials grow fast; try smaller n or a CAS for huge integers.
What does the Permutation & Combination on MyCalcsWorld actually compute?
Compute P(n,r) and C(n,r) for counting problems. You enter n, r, and the result panel updates in your browser.
What inputs does the Permutation & Combination need?
The Permutation & Combination asks for: n; r.
What results does the Permutation & Combination show?
The panel reports P(10,3), C(10,3). Each figure is recalculated whenever you change an input, so you can compare scenarios side by side.
How precise are the results?
Internal math uses JavaScript double precision; displayed values are rounded for readability. For proofs or high-stakes engineering, re-check with your required significant figures.