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Permutation and Combination Calculator

Use this permutation and combination calculator to summarize a data set for permutation and combination.

Primary answer
Count
Inputs to verify
Total distinct items, Items selected or positions, and Arrangement type
Use type
Use as an estimate that depends on assumptions.
Keyword intent
permutation and combination calculator

Calculator

Permutation and Combination Calculator

Calculates count from total distinct items, items selected or positions, arrangement type. Defaults are filled in so you can review a working example before changing inputs.

Number of distinct item types available, from 0 to 500.

Number selected or number of ordered positions, from 0 to 500.

Use permutation when order matters; use combination when order does not matter.

Choose whether an item type may be selected more than once.

Result

Result reflects the current submitted inputs.

  • Risk B
  • Reviewed 2026-05-26
  • 3 sources
Count720
Formula usedP(n,r) = n! / (n - r)!
Total items used10
Selection size used3

Breakdown

Arrangement type
permutation
Repetition
without
Formula used
P(n,r) = n! / (n - r)!
  • n is the number of distinct item types.
  • r is the number of selected items or ordered positions.
  • Permutation mode means order matters; combination mode means order does not matter.
  • Repetition mode means an item type can be selected more than once.
  • Duplicate labels in the original set are out of scope; users should first collapse to distinct item types.
  • Exact integer counts are returned as strings so large counts are not rounded.

Accuracy notes

Risk level
B
Reviewed
2026-05-26
Sources
3
Primary result
Count

Formula logic is kept in a pure calculator module with fixtures, source notes, and page-visible assumptions.

Categories

What the result means

Use Count as the headline answer for permutation and combination. Exact integer count returned as a string to avoid large-number rounding. Read the center or spread metric first, then compare count, minimum, maximum, and sample/population notes. Use formula used, total items used, and selection size used to explain why count moved when an input changed. Review the raw values and decide whether outliers or missing data should be handled before reporting the result.

CountExact integer count returned as a string to avoid large-number rounding.
Formula usedFormula selected from arrangement and repetition choices.
Total items usedValidated total number of distinct item types.
Selection size usedValidated selected items or ordered positions.

Use the result this way

  1. Start with Count, then use supporting outputs only to explain the primary answer.
  2. Verify total distinct items, items selected or positions, and arrangement type before copying the result.
  3. Choose the mode or method first because it can change which formula is applied and stay within the documented minimum and maximum ranges.
  4. Review the raw values and decide whether outliers or missing data should be handled before reporting the result.

User job

How to use this calculator

Use Permutation and Combination Calculator when you need count, then use formula used and total items used to check the context for data review, classwork, quality checks, and quick descriptive summaries.

Best for

  • Summarizing a list of values
  • Checking spread, center, or sample assumptions
  • Reviewing a default example before entering your own total distinct items and items selected or positions.

Check before relying

  • Confirm whether the data is a sample or population and whether outliers should stay in the list.
  • n is the number of distinct item types.
  • r is the number of selected items or ordered positions.
  • Source context: OpenStax, Rice University, reviewed 2026-05-26.

Next useful step

Formula

Counts permutations or combinations with optional repetition using nPr, nCr, n^r, or C(n + r - 1, r). Key assumptions: n is the number of distinct item types. r is the number of selected items or ordered positions. Permutation mode means order matters; combination mode means order does not matter.

  • Counts permutations or combinations with optional repetition using nPr, nCr, n^r, or C(n + r - 1, r).
  • n is the number of distinct item types.
  • r is the number of selected items or ordered positions.
  • Primary source context: OpenStax, Rice University.

Inputs

Enter total distinct items, items selected or positions, arrangement type, and repetition for data review, summaries, quality checks, and classwork. Before calculating, choose the mode or method first because it can change which formula is applied and stay within the documented minimum and maximum ranges. Total distinct items: Number of distinct item types available, from 0 to 500. Items selected or positions: Number selected or number of ordered positions, from 0 to 500. Arrangement type: Use permutation when order matters; use combination when order does not matter. Repetition: Choose whether an item type may be selected more than once.

Total distinct itemsNumber of distinct item types available, from 0 to 500.
Items selected or positionsNumber selected or number of ordered positions, from 0 to 500.
Arrangement typeUse permutation when order matters; use combination when order does not matter.
RepetitionChoose whether an item type may be selected more than once.

Example

Using the default inputs, Permutation and Combination Calculator returns count of 720. Adjust total distinct items, items selected or positions, arrangement type, and repetition to match your own scenario.

FAQ

How is count calculated here?

Counts permutations or combinations with optional repetition using nPr, nCr, n^r, or C(n + r - 1, r). The first assumption to check is: n is the number of distinct item types.

What does Count mean for permutation and combination?

Read the center or spread metric first, then compare count, minimum, maximum, and sample/population notes. Secondary values such as formula used, total items used, and selection size used are there to explain the primary answer, not to replace it.

What should I enter for Total distinct items?

Number of distinct item types available, from 0 to 500. Choose the mode or method first because it can change which formula is applied and stay within the documented minimum and maximum ranges.

How does Items selected or positions change count?

Number selected or number of ordered positions, from 0 to 500. Changing it can alter count because the formula uses the submitted inputs together. Also compare sample versus population mode, separators, missing values, outliers, and rounding precision.

Why does the permutation and combination example show 720 for count?

The default inputs produce 720 for count. Treat that as a format and scale check, then replace every default value with your own inputs.

What should I check before reporting count?

Confirm how the values were parsed, whether the data is a sample or population, and whether outliers or missing values should stay in the set.

Sources

Last reviewed: 2026-05-26

  • Reviewed 2026-05-26
    Contemporary Mathematics, Section 7.2: PermutationsOpenStax, Rice University. Permutation meaning, order-matters distinction, and nPr-style counting without repetition.
    Scope
    English-language textbook coverage of permutations and the multiplication principle.
    Supports
    Permutation meaning, order-matters distinction, and nPr-style counting without repetition.
    Limits
    Educational source; this calculator separately documents bounded input ranges and repetition modes.
  • Reviewed 2026-05-26
    Contemporary Mathematics, Section 7.3: CombinationsOpenStax, Rice University. Combination meaning, order-does-not-matter distinction, and nCr-style counting without repetition.
    Scope
    English-language textbook coverage of combinations.
    Supports
    Combination meaning, order-does-not-matter distinction, and nCr-style counting without repetition.
    Limits
    Educational source; combinations with repetition are additionally cross-checked against MathWorld.
  • Reviewed 2026-05-26
    Ball PickingWolfram MathWorld. The four formula cases used by this bounded MVP: nPr, nCr, n^r, and combinations with repetition.
    Scope
    Combinatorial counting cases for ordered/unordered selections with and without replacement.
    Supports
    The four formula cases used by this bounded MVP: nPr, nCr, n^r, and combinations with repetition.
    Limits
    Reference source; examples and UI assumptions are maintained in this package.

Disclaimer

This calculator is an educational estimate based on the inputs and assumptions shown on the page.