Quick guide
How to use this calculator
- Enter distinct item labels.
- Choose the selection size and whether order or repetition matters.
- 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.