Permutation & Combination (nCr, nPr) Calculator
About Permutation & Combination (nCr, nPr) Calculator
The Permutation & Combination Calculator helps you easily find the number of ways to arrange or select items. It’s especially useful for students preparing for math, statistics, and probability exams.
Formulas (Simple Explanation)›
Permutation (nPr) = n! / (n − r)! Combination (nCr) = n! / [r! × (n − r)!]
Where: n = total number of items, r = number of items selected. Use nPr for arrangements (order matters) and nCr for selections (order doesn’t matter).
Example:
Input: n = 5, r = 2
Output: nPr = 5! / (5−2)! = 20, nCr = 5! / (2! × 3!) = 10
Steps to Use:
- Enter the total number of items (n).
- Enter the number of items selected (r).
- Click 'Calculate' to get both nPr (permutation) and nCr (combination).
- Use results for probability, counting, or exam questions.
Frequently Asked Questions
What is the difference between permutation and combination?›
Permutation refers to arrangements where order matters (like seat arrangements), while combination refers to selections where order doesn’t matter (like choosing a team).
What does n and r stand for in nCr or nPr?›
In these formulas, n is the total number of items, and r is the number of items being selected or arranged.
Where are permutations and combinations used?›
They are used in probability, statistics, game theory, and real-world problems like lotteries, seating arrangements, and password creation.
Can I use this calculator for large values of n and r?›
Yes. The calculator can handle big numbers easily using factorial computation, but very large values may round for readability.
Is there a shortcut to remember the difference?›
Yes. Think: 'P' for positions (order matters), 'C' for choices (order doesn’t matter).