Combination Calculator Formula

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

Use the Combination Calculator

Formulas Used

C(n, r)

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

P(n, r) for comparison

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)!)

A combination counts the number of ways to choose r items from n distinct items where order does not matter. For example, choosing 3 team members from 10 candidates is a combination problem because the group {A, B, C} is the same regardless of selection order.

Worked Example

How many ways can you choose a committee of 3 from 10 people?

n = 10r = 3
  1. 01C(10, 3) = 10! / (3! * 7!)
  2. 02= (10 * 9 * 8) / (3 * 2 * 1)
  3. 03= 720 / 6 = 120
  4. 04Compare with permutations: P(10,3) = 720

Ready to run the numbers?

Open Combination Calculator