Use this exact counting tool when the selection order, repetition rule, and integer domain are unambiguous.

Total items

Required integer input.

Chosen items

Required integer input.

Calculate the number of ordered ways to choose k items from n items. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Permutations

The resulting permutations returned as an integer.

• Combinatorial counts grow rapidly and may exceed practical enumeration or supported integer ranges. Similar-looking formulas answer different questions when order or repetition changes.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

State whether order matters and whether repetition is allowed before selecting a formula. For large results, use arbitrary-precision arithmetic or logarithms and avoid generating every arrangement unnecessarily.

• Combination Count Calculator

  Calculate the number of unordered ways to choose k items from n items.

• Catalan Number Calculator

  Compute the nth Catalan number using the multiplicative formula.

• Double Factorial Calculator

  Calculate the double factorial of a nonnegative integer.