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Permutation & Combination Calculator – nPr/nCr with Repetition and Comparison

Compute permutations and combinations, compare order vs orderless counts, handle repetition, see ratios, formulas, previews, and educational insights client-side.

No uploads. Everything runs locally in your browser.

Status

Example loaded. Adjust values and calculate.

n: 5r: 3Repetition: WithoutTotal outcomes: 60
Quick insights
  • Order matters? Yes for permutation
  • Repetition: Not allowed
  • Permutation/Combination ratio: 6
  • Probability (one outcome): Perm 1 / 60 | Comb 1 / 10
Results
Permutation: 60
Combination: 10
Ratio (perm/comb): 6
Permutation formula: 5P3 = 5! / (5-3)!
Combination formula: 5C3 = 5! / (3! (2)!)
Comparison table (nearby r)
rPermutationCombination
155
22010
36010
41205
51201
Sample outcomes (labels)
Permutations
ABC
ABD
ABE
ACB
ACD
ACE
ADB
ADC
ADE
AEB
AEC
AED
Combinations
ABC
ABD
ABE
ACD
ACE
ADE
BCD
BCE
BDE
CDE
Explanation
Permutation (without repetition): 5P3 = 5! / (5-3)!
Combination (without repetition): 5C3 = 5! / (3! (2)!)

What is this tool

The Permutation & Combination Calculator counts ordered arrangements (nPr) and unordered selections (nCr), with options for repetition and a compare mode. It shows formulas, ratios, probabilities, and previews when you provide small label sets. Use it for team selection, seating/ranking outcomes, lottery/card examples, or password-style counts — all computed instantly in your browser.

Educational extras include nearby r comparison, permutation/combination repetition formulas, symmetry insight (nCr = nC(n−r)), and probability helpers so students and teams can pick the right model (order vs orderless, with vs without repetition).

Use cases

  • Plan team or committee selections (orderless combinations).
  • Estimate seating or podium arrangements where order matters (permutations).
  • Model lottery/card draws and password-style counts with or without repetition.
  • Teach combinatorics with formula breakdowns and small previews.
  • Compare outcome growth as r changes using the nearby r table.

These scenarios appear in classroom combinatorics practice, event planning, product ranking, and probability problems. Clear formulas and previews keep mistakes low and explanations crisp.

Popular ways to use this tool

  • Compare permutations vs combinations for the same n and r.
  • Use repetition mode to approximate password or code counts.
  • Share ratio and probability insights in homework or reports.
  • Preview sample orders/groups with provided labels to illustrate outcomes.
  • Show symmetry (nCr = nC(n−r)) and nearby r changes to students.

Copyable summaries, explanations, and previews let you drop results into docs, chats, or slides without recomputing. The calculator keeps combinatorics fast, visual, and educational.

How to use Permutation & Combination Calculator

  1. Enter n (total items) and r (selected items); optionally add item labels.
  2. Choose mode (Permutation, Combination, Compare) and repetition option.
  3. Click Calculate to see results, formulas, ratios, and sample outcomes when small.
  4. Copy results or explanations; use Fill example or Clear to reset.

Key features of Permutation & Combination Calculator

  • nPr/nCr with and without repetition, plus compare mode
  • Formulas, factorial breakdown, ratio, and probability helper
  • Mini result table for nearby r values and symmetry insight for combinations
  • Optional labeled item previews (capped for small sets)
  • Copy summary/explanation/previews, example fill, clear/reset with responsive layout

Permutation & Combination Calculator — key benefits

  • Completely free with no signup or registration required.
  • Runs entirely in your browser — your data is never uploaded.
  • Works on desktop, tablet, and mobile devices.
  • Instant results with no waiting or processing queues.
  • Part of the ToolCircuit suite of free online math tools tools.

FAQ

Do you support repetition?

Yes. Permutation with repetition uses n^r; combination with repetition uses (n+r-1)Cr.

What if r > n?

Without repetition, r must be ≤ n. With repetition, r can exceed n since items can repeat.

Can I see both permutation and combination together?

Use Compare mode to see both counts side by side, including their ratio and probabilities.

Do you generate sample outcomes?

Yes, when labels are provided and the set is small (≤6 items, r ≤3) to avoid performance issues.

Is this calculator free?

Yes. It runs locally in your browser with no login or uploads.

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