What is the difference between permutation and combination?

A permutation counts arrangements where order matters (ABC is different from CBA), while a combination counts selections where order doesn't matter (ABC is the same as CBA). Permutations always yield a larger number than combinations for the same n and r values, because they account for all possible orderings.

nPr stands for the number of permutations of r items chosen from n items. The formula is n! / (n-r)!, where ! denotes factorial. For example, 5P3 = 5! / 2! = 60, meaning there are 60 ways to arrange 3 items selected from 5 when order matters.

nCr stands for the number of combinations of r items chosen from n items. The formula is n! / (r! × (n-r)!), which divides the permutation count by r! to account for the fact that order doesn't matter. For example, 5C3 = 5! / (3! × 2!) = 10.

Can this calculator handle large values of n?

Yes, the calculator uses BigInt for factorial calculations, which avoids the precision limitations of standard JavaScript numbers. It can accurately compute permutations and combinations for n values well into the hundreds, producing exact results even for very large numbers.

Factorial (denoted by !) is the product of all positive integers up to a given number. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1. Factorials grow extremely quickly — 10! is already 3,628,800. They are the building blocks of permutation and combination formulas.

How do I know whether to use permutation or combination?

Ask yourself: does the order of selection matter? If yes, use permutation (nPr). If no, use combination (nCr). For example, choosing a committee (order doesn't matter) uses combinations, while choosing officers with specific roles (order matters) uses permutations.

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Permutation & Combination Calculator

A permutation and combination calculator computes nPr (arrangements where order matters) and nCr (selections where order doesn't matter) using the formulas n!/(n-r)! and n!/(r!×(n-r)!). It also provides step-by-step factorial breakdowns for each calculation.

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What is Permutation & Combination Calculator?

A permutation and combination calculator is a mathematical tool that computes the number of ways to arrange (nPr) or select (nCr) items from a set, using factorial-based formulas fundamental to combinatorics and probability.

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The permutation and combination calculator brings mathematical precision to combinatorics problems, with BigInt-powered accuracy that handles even the largest inputs. Its dual calculation of nPr and nCr, combined with detailed step-by-step breakdowns, makes it equally valuable for students learning the concepts and professionals working with complex combinatorial problems. This tool transforms a potentially error-prone manual process into an instant, reliable calculation.

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