Free Discrete Math Calculators

Combination Calculator — nCr & n Choose r

Calculate C(n,r) combinations without repetition, C̄(n,r) with repetition, P(n,r) permutations, and nʳ — all in one tool. Supports BigInt exact arithmetic for large n, step-by-step working, Pascal's triangle, combination listing, and session persistence.

Permutation Calculator — nPr

Calculate the number of permutations where order matters.

Boolean Algebra Calculator

Evaluate Boolean expressions with AND, OR, NOT, XOR, NAND, NOR, XNOR, implication, and biconditional. Generates truth tables for up to 4 variables with SOP, POS canonical forms, Σm/ΠM notation, and equivalence checking.

Combinations with Repetition — Stars & Bars

Calculate multiset combinations C̄(n,r) = C(n+r−1,r) where repetition is allowed. Features stars & bars visualization, step-by-step working, multiset listing, all four combinatorial variants, BigInt exact arithmetic, and session persistence.

Pascal's Triangle Calculator

Generate Pascal's triangle up to any row and expand (a + b)ⁿ using the binomial theorem. Shows all coefficients and the full polynomial expansion.