Combinatorics Calculator
Calculate permutations, combinations, and solve counting problems
Basic Counting
Combinatorics studies ways to count finite discrete structures, providing formulas for permutations, combinations, and other counting problems.
Advanced Counting
Advanced counting techniques help solve more complex counting problems.
Formulas Reference
Factorial
n! = n × (n-1) × (n-2) × ... × 2 × 1
The number of ways to arrange n distinct objects in a row.
Permutation
P(n,r) = n! / (n-r)!
The number of ways to arrange r objects from a set of n distinct objects, where order matters.
Combination
C(n,r) = n! / (r! × (n-r)!)
The number of ways to select r objects from a set of n distinct objects, where order doesn't matter.
Catalan Number
Cn = (1/(n+1)) × C(2n,n)
Appears in many counting problems like the number of valid parentheses expressions.