Permutation & Combination Calculator
About the Permutation & Combination Calculator
The Permutation and Combination Calculator is a mathematical tool used to calculate the number of possible arrangements and selections of objects. These concepts form the foundation of counting techniques in probability, statistics, and combinatorics and are widely used in mathematics, computer science, data analysis, and competitive examinations.
A permutation refers to the arrangement of objects where the order matters. In contrast, a combination refers to the selection of objects where the order does not matter. This calculator computes both values using standard mathematical formulas, helping users clearly understand the difference between the two.
How to Use This Calculator
To use the calculator, enter the total number of items (n) and the number of items to be selected (r). After clicking the Calculate button, the calculator instantly displays both permutation (nPr) and combination (nCr) results.
The calculator automatically applies the formulas:
Permutation: nPr = n! / (n − r)!
Combination: nCr = n! / [r! (n − r)!]
Example
If n = 5 and r = 3:
Permutation (5P3) = 60
Combination (5C3) = 10
This means there are 60 different arrangements but only 10 different selections.
This calculator saves time, reduces calculation errors, and is especially useful for students preparing for entrance exams, probability problems, and logical reasoning tests. It also helps users build a clear conceptual understanding of how permutations and combinations differ in practical applications.
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