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Permutation & Combination Calculator

Calculate the number of possible arrangements (permutations) or selections (combinations).

Combinatorics Tool

Calculate possible arrangements and combinations.

Permutations (nPr) care about order; Combinations (nCr) do not.

Understanding the Permutations & Combinations Calculator

Instantly calculate the number of ways to arrange or group items. Our tool provides precise values for nPr and nCr while visualizing how these totals grow relative to your subset size.

Guide

How to use the Permutations & Combinations Calculator

  • 1Enter the 'Total Items (n)' which is the full size of your set.
  • 2Enter the 'Selected Items (r)' which is how many you want to choose.
  • 3Click 'Calculate Results' to see the arrangements.
  • 4Observe the Chart below to see how the number of combinations vs. permutations changes as you select more items.
Applications

Common Use Cases

Games & Gambling: Calculating possible poker hands or lottery combinations.
Cybersecurity: Determining the difficulty of cracking a multi-character password.
Project Management: Finding the number of possible sub-teams from a large department.
Probability: Establishing the denominator for complicated probability fractions.

The Maths Behind the Calculation

nPr = n! / (n-r)! | nCr = n! / (r!(n-r)!)

Permutations account for every unique sequence, while Combinations divide out the redundantly ordered groups.

Knowledge Base

Frequently Asked Questions

When should I use Permutation?

Use permutations when order matters—like the sequence of digits in a PIN or the first, second, and third place in a contest.

When should I use Combination?

Use combinations when the order doesn't matter—like a hand of cards or a fruit salad with three ingredients.

What is the largest value I can calculate?

This tool uses standard floating-point math. Extremely large factorials (like 200!) will result in 'Infinity' due to standard computer memory limits.

Regional Notice: United States

"Federal tax estimates are based on 2024 brackets. Consult a tax professional for official filing."