Math

Combinations and Permutations Calculator

Count selections and ordered arrangements without repetition using exact integer arithmetic.

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How to use Combinations and Permutations Calculator

Combinations C(n,k) count unordered selections; permutations P(n,k) count ordered selections. Both assume distinct items and no repetition.

Whole numbers only: 0 ≤ k ≤ n ≤ 1,000. Output integers are exact and may contain thousands of digits.
Decimal inputs have at most 120 characters and magnitude from 1e-100 to 1e15, or zero. Floating-point results are rounded to 12 significant digits; extreme derived results may underflow or be rejected. Exact integer results are identified separately.

What calculation does Combinations and Permutations Calculator perform?

Combinations C(n,k) count unordered selections; permutations P(n,k) count ordered selections. Both assume distinct items and no repetition.

Does order matter?

Order matters for permutations. Selecting A then B differs from selecting B then A; combinations count that selection once.

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