Permutation Calculator
Compute permutations A(n,r), list all arrangements, and show the formula
📐 排列数 A(n, r)
💡 公式：A(n, r) = n! / (n-r)!，表示从 n 个不同元素中取 r 个的排列数
About this tool
The permutation calculator counts arrangements and can list them all:
- Count: enter n and r to compute A(n,r) = n!/(n-r)! with the formula and working shown
- List all: enter a set of items and generate every arrangement, up to 8 items
- Total: the number of permutations is displayed
- Copy: each arrangement can be copied
Permutation formula
Choosing r items from n distinct items in order gives A(n,r) = n! / (n-r)!. When r equals n this is the full permutation A(n,n) = n!.
When to use it
- Probability and combinatorics
- Counting possible passwords or codes
- Counting queue orders and arrangement plans
- Math homework help
Formula notes
- Permutations: A(n,r) = n! / (n-r)!, where order matters
- Full permutation: A(n,n) = n!, every ordering of n items
- Versus combinations: permutations count order, combinations do not
- Growth: 8 items give 40320 orderings and 10 items give 3628800, so listing is capped for performance