Combinatorics calculator

Input
Result

Input

Total items n

Chosen items k

Try an example

Choose the right modelUse combinations for an unordered group and arrangements for ordered positions. Repetition means an item can be chosen more than once. Counts use exact integers within the supported calculation limit; n and k must be whole numbers from 0 to 100000. This is not a probability calculation.

Result

Arrangements nPk

720

Combinations nCk

120

With repetitions

1,000

Combinations with repetitions

220

Formula: nPk = n!/(n-k)!, nCk = n!/(k!(n-k)!)

Formula	nPk = n!/(n-k)!, nCk = n!/(k!(n-k)!)

Selection type

Selection type: Arrangements nPk
Order matters: Yes
Repetition allowed: No
Formula: n! / (n − k)!
Value: 720

Selection type: Combinations nCk
Order matters: No
Repetition allowed: No
Formula: n! / (k! × (n − k)!)
Value: 120

Selection type: With repetitions
Order matters: Yes
Repetition allowed: Yes
Formula: nᵏ
Value: 1,000

Selection type: Combinations with repetitions
Order matters: No
Repetition allowed: Yes
Formula: C(n + k − 1, k)
Value: 220

Selection type	Order matters	Repetition allowed	Formula	Value
Arrangements nPk	Yes	No	n! / (n − k)!	720
Combinations nCk	No	No	n! / (k! × (n − k)!)	120
With repetitions	Yes	Yes	nᵏ	1,000
Combinations with repetitions	No	Yes	C(n + k − 1, k)	220

Combinations and permutations calculator

Use the calculator for probability tasks, education, testing scenarios and quick combinatorics checks.

Very large n and k can produce huge values, so results are formatted as estimates by the browser.

Quick start

Compare ordered and unordered selections, with or without repetition.

Enter whole values n and k
Calculate and compare the four selection models
Copy or export the exact supported results

✓ Use the calculator to turn input values into a clear, repeatable result.

✓ Keep units and assumptions visible so the calculation can be checked later.

✓ Copy the result or key numbers for reports, messages or spreadsheets.

✓ Reset to defaults when you want to compare another scenario from a clean state.

✓ Calculators run in the browser and are useful for quick estimates before formal checks.

✓ For finance, health, engineering or legal decisions, verify important results with a specialist or official source.

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