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Combination Calculator

Enter your values below to get the result first, then scroll for the full explanation and guidance.

Step 1 • Add values

Use the calculator

Enter your values below to generate an instant result. You can update the inputs at any time to compare different scenarios.

Example: choosing 3 items from 10 gives 120 combinations.

Results refresh instantly as values change.

Combinations

120Order does not matter

Combinations: 120 (Order does not matter)

There are 120 ways to choose 3 items from 10 without regard to order.

Combination result

There are 120 ways to choose 3 items from 10 without regard to order.

Result snapshot

A quick visual read of the values behind this result.

Population (n)10
Selections (r)3

Recommended next checks

  • →Use permutations instead when the order of selected items matters.
Population (n)
10
Selections (r)
3

Try different values to compare results.

Enter n and r to calculate how many different unordered selections are possible.

Fast to use

Built for comparison

Clear result output

Table of Contents

6

About Combination Calculator

Combination Calculator helps you work through the main numbers for this topic quickly with a simple input flow and an instant result.

Use the calculator result as a practical starting point, then review the explanation and assumptions on the page if you want more context.

Combination formula

n choose r = n! / (r! x (n-r)!). The implementation cancels factors progressively to retain an exact integer.

Formula explained

Calculation flow

This calculator is structured for fast UK-focused estimates with clear inputs, repeatable logic, and instant results.

Formula

Input values -> calculation engine -> instant result

How the result is built

1Enter the values requested in the form.
2The calculator applies the configured formula logic.
3The result updates instantly with a breakdown.
4Use the output to compare scenarios quickly.

Example

Example: choosing 3 items from 10 gives 120 combinations.

Assumptions

  • n and r are whole numbers, 0 <= r <= n <= 1,000.
  • Order does not matter and items are selected without replacement.

Source basis

  • UK-focused calculator flow
  • Structured input validation
  • Instant result breakdowns

FAQ

Common questions

Use permutations when different orders of the selected items count as different outcomes.

Trust and notes

Assumptions and important notes

This calculator is designed to give a fast estimate using the method shown on the page. Results are most useful when your inputs are accurate and the tool matches your situation.

Use the result as guidance rather than a final diagnosis or professional decision. If the result could affect health, legal, financial, or compliance decisions, verify it with a qualified source where appropriate.

  • n and r are whole numbers, 0 <= r <= n <= 1,000.
  • Order does not matter and items are selected without replacement.

Method

UK calculator guidance

Last reviewed

April 17, 2026