Permutation calculator

Calculate permutations of distinct or repeated elements. Exact integer answers for up to 1,000 elements, without rounding.

Your inputs stay herePUFFINMINT

Set your data

Number of elements n (0–1000)

Permutation type

Sizes of all groups (e.g. 2; 2)

Choose distinct elements for n!, or repeated elements. For repetitions enter the size of every group, including groups of one.

Enter your data and run the tool. Your result will appear here.

Follow the effect of repeated items on the count.

The values you enter stay on this page. Reloading or closing it clears them.

We count which tools are used most, without including entered values or file contents in the statistics. Privacy

P = n!

For n distinct elements P=n!. For indistinguishable groups of sizes n₁,…,nₖ, P=n!/(n₁!×…×nₖ!).

P = \frac{n!}{n_{1}! \times … \times n_{k}!}

ANNA has groups 2; 2, giving 4!/(2!×2!)=6 distinct arrangements. Four different elements give 24 arrangements.

Input

Result

4 \times 3 \times 2 \times 1 = 24

Group sizes must be positive integers summing to n. This counts arrangements of all elements, not selections of k elements. By convention 0!=1.

Limits and checks
Parameter	Value
Number of elements n (0–1000)	≥ 0; ≤ 1000