Combinatorics
Browse our collection of combinatorics calculators.
Combinatorics Calculator
Calculate combinations C(n,r), permutations P(n,r), and factorials n! with detailed explanations and step-by-step solutions
Binomial Coefficient Calculator
Calculate binomial coefficients C(n,k) with Pascal's triangle visualization and properties
Fibonacci Sequence Calculator
Calculate Fibonacci numbers with golden ratio connection and sequence visualization
Catalan Numbers Calculator
Calculate Catalan numbers with applications in combinatorics and binary trees
Modular Arithmetic Calculator
Perform modular arithmetic operations including addition, multiplication, exponentiation, and modular inverse calculations.
Derangements Calculator
Calculate the number of derangements (permutations with no fixed points) and analyze the subfactorial function.
What is Combinatorics?
Combinatorics is the branch of mathematics concerned with counting, arranging, and selecting objects. It answers questions like "How many ways?" and "How many possibilities?"
- Combinations (C): Selecting items where order doesn't matter (choosing team members)
- Permutations (P): Arranging items where order matters (ranking contestants)
- Factorials (!): Product of all positive integers up to n (arranging all items)