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Permutations & Combinations Calculator

Count ordered or unordered selections, with or without replacement, using exact integers.

Your numbers

Make it your own
Updates as you type
Number of arrangements
120

Calculated from your inputs · rounded for display

Order matters?No
Repetition allowed?no

Your calculation, step by step

No black boxes
  1. C(n,k) = n! / (k!(n−k)!)
  2. The empty selection has one arrangement.

How to use this calculator

  1. Enter your own values in the labeled fields. Check the units and assumptions before comparing results. Only the fields needed for your selected calculation mode are shown.
  2. Your answer updates automatically. Review the calculation steps to see exactly how it was calculated.
  3. Copy, share, save, or download your result. Saved inputs stay on this device.

How the calculation works

nCr=n!/[k!(n−k)!]; nPr=n!/(n−k)!; repetition: C(n+k−1,k) or n^k

Combinations ignore ordering; permutations distinguish it. With replacement a type can appear repeatedly, so a different formula applies. n and k are bounded nonnegative integers; selecting no objects has one arrangement. Review the units, period and assumptions before comparing scenarios. Displayed values are rounded, while the underlying calculation retains its available precision.

A worked example

Selecting 3 from 10 without replacement gives C(10,3)=120 combinations or P(10,3)=720 ordered arrangements.

Reading your result

Use the main result together with its units and supporting figures. Display values are rounded; calculations keep their underlying precision. A change in inputs or assumptions can change the answer. Compare the step-by-step working with your intended use before relying on an estimate.

Frequently asked questions

What assumptions does this calculation use?

Combinations ignore ordering; permutations distinguish it. With replacement a type can appear repeatedly, so a different formula applies. n and k are bounded nonnegative integers; selecting no objects has one arrangement.

Can I save or check a scenario?

The result includes the working and supporting values. Save and Restore keep inputs on this device; Copy, Download and Print export the result. Sharing a scenario explicitly includes the inputs in its link.

Sources & methodology

This calculator uses the mathematical identity and assumptions stated above. No current rates, prices, or external data are loaded. Conversion tools use international unit definitions.

Formula review: October 24, 2026. Read our methodology.