Permutations & Combinations Calculator Online | Combinatorics Tool

Free online permutation combination calculator for computing the number of possible arrangements (permutations) or selections (combinations) from a set of objects. This comprehensive combinatorics calculator and counting calculator provides instant results for mathematical and statistical analysis.

Typical Use Cases

Our permutation combination calculator online serves as an essential combinatorics calculator for mathematics students, statisticians, and probability professionals. Students use this arrangement calculator for homework verification in discrete mathematics, probability theory courses, and statistical analysis requiring precise counting calculations.

Data scientists and researchers rely on this selection calculator for genetics analysis (DNA sequence permutations), game theory applications, market research sampling, and sports analytics team arrangement scenarios. Business analysts use this combinatorics tool for inventory management, quality control testing, and strategic decision-making involving multiple variable combinations.

Formula

Permutation (nPr): P(n,r) = n! / (n-r)! - Order matters
Combination (nCr): C(n,r) = n! / (r! × (n-r)!) - Order doesn't matter
Factorial (n!): n! = n × (n-1) × (n-2) × ... × 2 × 1