Discrete Math Calculators

Calculate combinations without replacement. Step-by-step solution with formula, example dataset and interpretation guide.

Calculate permutations without replacement. Step-by-step solution with formula, example dataset and interpretation guide.

Calculate factorials of integers. See formula, step-by-step solution and all rearrangements. Instant math solver.

Generate Pascal's Triangle for any number of rows. Enter n — see the full triangle with binomial coefficients and pattern highlights. Free.

Generate Fibonacci sequence numbers. See formula, step-by-step solution and all rearrangements. Instant math solver.

Calculate combinations with replacement C(n+r−1, r). Enter n and r — get the result with stars-and-bars formula and examples. Free.

Calculate permutations with replacement (nʳ). Enter n and r — get the count with formula and comparison to permutations without replacement. Free.

Calculate combinations nCr for any n and r. Enter values — see the binomial coefficient, formula, and Pascal's triangle position. Free.

Apply the Inclusion-Exclusion Principle to count elements in unions of sets. Enter set sizes and overlaps — get the union count with steps. Free.

Calculate Stirling numbers of the first or second kind. Enter n and k — get the Stirling number with combinatorial interpretation. Free.

Calculate the nth Catalan number. Enter n — get the Catalan number with recursive formula, closed form, and combinatorial interpretation. Free.

Calculate derangements (permutations with no fixed points) for n objects. Enter n — see D(n) with subfactorial formula and probability. Free.