Combination Calculator Formula

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

Use the Combination Calculator

Formulas Used

Combinations

combinations = factorial(n) / (factorial(r) * factorial(n - r))

Permutations

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

Variables

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

How It Works

How to Calculate Combinations

Formula

C(n, r) = n! / (r! × (n - r)!)

Where:

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

    • Combinations count selections where order does not matter.

    Worked Example

    How many ways can you choose 3 items from a set of 10? (Order does not matter)

    n = 10r = 3
    1. 01C(10, 3) = 10! / (3! × 7!)
    2. 02= 3,628,800 / (6 × 5,040)
    3. 03= 3,628,800 / 30,240
    4. 04= 120

    Ready to run the numbers?

    Open Combination Calculator