CALCULATE WITH CONFIDENCE

Counting, Permutations & Combinations

Permutation & Combination Generator

Generate actual arrangements or selections from a short list of distinct items.

Counting & Combinatorics

Generate selections from your own items

Up to 500 displayed rows
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Separate items with commas, semicolons, or line breaks.

Total selections

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Enter valid values to see the result.

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Understand the subject

What does the selection generator show?

The generator turns a finite counting rule into the actual allowed selections or arrangements. It lets you inspect the objects behind an exact count.

Use it for small labelled lists when seeing the cases matters as much as knowing their total.

The relationship

The counting rule

See the structure

A finite tree becomes a list of cases

Worked example

Check the rule with a small case

From red, green, and blue, unordered pairs are {red, green}, {red, blue}, {green, blue}.

Interpret with care

Choose the right counting model

The display is deliberately capped. A capped list never means the exact count was capped.

Use the Permutation & Combination Generator when a small case needs to be inspected rather than only counted.

Quick guide

How to use this calculator

  1. Enter distinct item labels.
  2. Choose the selection size and whether order or repetition matters.
  3. Compare the exact count with the generated rows.

Calculation method

Traverse the finite selection tree

The generator visits each allowed next item according to the selected order and repetition rules. Counting remains exact even when display output is capped.

Worked example

Choose two colors

From red, green, and blue there are three unordered pairs without repetition.

{red, green}, {red, blue}, {green, blue}

Supported inputs

Precision and limits

Discrete domain

Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.

Exact integers

Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.

Generation

Up to 12 distinct input items are accepted and at most 500 generated rows are displayed.