Permutation calculator
Calculate permutations of distinct or repeated elements. Exact integer answers for up to 1,000 elements, without rounding.
Choose distinct elements for n!, or repeated elements. For repetitions enter the size of every group, including groups of one.
Result
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How to use this calculator
Choose distinct elements for n!, or repeated elements. For repetitions enter the size of every group, including groups of one.
Formula and method
For n distinct elements P=n!. For indistinguishable groups of sizes n₁,…,nₖ, P=n!/(n₁!×…×nₖ!).
Worked example
ANNA has groups 2; 2, giving 4!/(2!×2!)=6 distinct arrangements. Four different elements give 24 arrangements.
Limits and interpretation
Group sizes must be positive integers summing to n. This counts arrangements of all elements, not selections of k elements. By convention 0!=1.
Frequently asked questions
How should I interpret the result?
ANNA has groups 2; 2, giving 4!/(2!×2!)=6 distinct arrangements. Four different elements give 24 arrangements.
What inputs and assumptions are required?
Group sizes must be positive integers summing to n. This counts arrangements of all elements, not selections of k elements. By convention 0!=1.