Combinations with Repetition Calculator

Enter n object types and selection size r to calculate C(n+r−1,r) exactly.

Distinct object types n

Selection / sequence size r

—Combinations with repetition

C(n+r−1,r)

For responsive browser use, n and r are capped at 5,000. Very large exact counts are abbreviated on screen.

Core describe → test → interpret workflows

Use descriptive context first, choose the method that matches the design, then keep inputs, settings and result evidence reproducible instead of copying a p-value without its analysis recipe.

Start: Statistics Calculator Choose a statistical test

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Stars-and-bars combination evidence

Count unordered selections with replacement using C(n+r−1,r), then expose the stars-and-bars parameters and how the count grows as the selection size changes.

Item types nSelections r

—Combinations

—n+r−1

—Bars

—Stars

Ready.

r	C(n+r−1,r)	Stars	Bars

Interpret statistical results in context

Use plots and descriptive summaries before formal tests. Check the sampling/design assumptions that matter for the chosen method, report effect size and uncertainty where available, and avoid treating a threshold such as p < .05 as proof of importance, causation, or truth. Browser calculations are educational/planning utilities, not domain-specific professional advice.

How to use this Combinations with Repetition Calculator

Enter n object types and selection size r to calculate C(n+r−1,r) exactly.