Combinations and Permutations Calculator
Calculate the number of combinations and permutations.
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Calculate Combinations and Permutations
Our Combinations and Permutations Calculator helps you find the number of ways to choose or arrange a subset of items from a larger set, a key concept in probability and statistics.
What are Combinations and Permutations?
Combinations and permutations are two fundamental concepts in combinatorics, the branch of mathematics dealing with counting. **Permutations** are arrangements where the order of selection matters. **Combinations** are selections where the order does not matter. This calculator helps compute both, which is essential for solving problems in statistics, probability, and computer science.
How It Works: The Formulas
The calculator uses the standard factorial-based formulas:
Permutation (nPr): n! / (n - r)!
Combination (nCr): n! / [r! (n - r)!]
Where 'n' is the total number of items, and 'r' is the number of items you are choosing.
Frequently Asked Questions
What is the difference between a combination and a permutation?
The key difference is order. In a permutation, the order of the items matters (e.g., a lock combination like '1-2-3' is different from '3-2-1'). In a combination, the order does not matter (e.g., choosing three fruits for a salad - apple, banana, cherry is the same as cherry, banana, apple).
How do you calculate permutations?
The formula for permutations is nPr = n! / (n - r)!, where 'n' is the total number of items and 'r' is the number of items to choose. Our calculator automates this calculation.
How do you calculate combinations?
The formula for combinations is nCr = n! / (r! * (n - r)!), where 'n' is the total number of items and 'r' is the number of items to choose. This formula removes the duplicate arrangements that permutations would count.
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