Permutation Calculator Formula

Understand the math behind the permutation calculator. Each variable explained with a worked example.

Use the Permutation Calculator

Formulas Used

Permutations

permutations = factorial(n) / factorial(n - r)

N Factorial

n_factorial = factorial(n)

N Minus R Factorial

n_minus_r_factorial = factorial(n - r)

Variables

VariableDescriptionDefault
nTotal Items (n)10
rItems Chosen (r)3

How It Works

How to Calculate Permutations

Formula

P(n, r) = n! / (n - r)!

Where:

  • n = total number of items
  • r = number of items being chosen
  • ! = factorial

    • Permutations count arrangements where order matters.

    Worked Example

    How many ways can you arrange 3 items from a set of 10? (Order matters)

    n = 10r = 3
    1. 01P(10, 3) = 10! / (10-3)!
    2. 02= 10! / 7!
    3. 03= 10 × 9 × 8
    4. 04= 720

    Ready to run the numbers?

    Open Permutation Calculator