What is the Difference Between Combination and Permutation?

When selecting items from a group, the difference lies in whether the order of selection matters.

• Combination (nCr): Order does NOT matter. Selecting "A, B, C" is the same as "C, B, A". (Example: Lottery numbers, picking a team).
• Permutation (nPr): Order DOES matter. "A, B, C" is different from "C, B, A". (Example: Password codes, race winners).

Formulas Used in this Tool

Our Advanced Combination Calculator uses the following mathematical formulas:

• Combination: nCr = n! / (r! * (n-r)!)
• Permutation: nPr = n! / (n-r)!
• Combination with Repetition: (n+r-1)! / (r! * (n-1)!)
• Permutation with Repetition: n^r

Frequently Asked Questions (FAQ)

Can this calculator handle large numbers?

Yes! Unlike standard calculators that error out with "Infinity" on values like 1000!, our tool uses a custom BigInt engine to process unlimited digits accurately.

How do I save my calculations?

Your history is automatically saved in your browser. You can also click the CSV or PDF buttons to download a report of your work.