Permutation Calculator Formula

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

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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

    Frequently Asked Questions

    What is a permutation?

    A permutation is an arrangement of objects where the order matters. For example, the arrangements ABC and BAC are different permutations.

    What is the difference between permutation and combination?

    Permutations count arrangements where order matters (ABC ≠ BAC). Combinations count selections where order does not matter (ABC = BAC).

    Learn More

    Guide

    How to Calculate Probability - Complete Guide

    Learn the fundamentals of probability including basic probability, compound events, conditional probability, Bayes' theorem, and expected value with worked examples.

    Ready to run the numbers?

    Open Permutation Calculator