Calculate combination

Count ordered and unordered selections, with and without replacement.

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ToolCombination Calculator

Input

Output

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How it works

Factorial products compute permutations and combinations, with separate formulas for repeated selection. Symmetry reduces n choose r to only min(r, n−r) product steps before division.

All four counts appear because order and replacement describe the sampling process.
Inputs must be whole numbers with 0 ≤ r ≤ n.

Worked example

Choosing 2 from 5

All four variants for n = 5, r = 2

Input

											N: 5
R: 2

Output

												Permutations without repetition: 20
Combinations without repetition: 10
Permutations with repetition: 25
Combinations with repetition: 15

When to use this

Committee counts use unordered selection, PIN exercises use ordered choices with repetition, and card-hand calculations use combinations without replacement.

Edge cases

Choosing five items from three without replacement is rejected because r exceeds n.
Repeated source items require multiset counting; these formulas assume n distinct item types.
Counts beyond JavaScript’s safe-integer range are rejected instead of printing a rounded integer as exact.