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Math

Combinations Calculator

Count unordered selections of k distinct items from n items without replacement.

Exact method explained belowEditable inputs

Set up your calculation

Runs on your device

SOLUTION

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter available items n, selected items k.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

C(n,k) = n! ÷ [k!(n − k)!]. Equivalent selections in different orders count only once.

A WORKED EXAMPLE

Choosing 3 items from 10 gives 120 combinations.

What to keep in mind

Inputs are whole numbers with 0 ≤ k ≤ n ≤ 500. Items are distinct, and repetitions are not allowed.

Common questions

Does order matter?

No. Choosing A, B and C is the same selection as C, A and B.

What if I choose zero items?

There is one empty selection, so C(n,0) = 1.

Methodology maintained by ClarityKit. How these tools are built and checked.