Combination Calculator Formula

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

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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

    Frequently Asked Questions

    What is a combination?

    A combination is a selection of objects where the order does not matter. Choosing {A, B, C} is the same as choosing {C, B, A}.

    Where are combinations used?

    Combinations are used in lottery calculations, committee selections, card hands (e.g., poker), and any scenario where you select items without regard to order.

    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?

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