Examples for


Combinatorics is a branch of mathematics dealing primarily with combinations, permutations and enumerations of elements of sets. It has practical applications ranging widely from studies of card games to studies of discrete structures. Wolfram|Alpha is well equipped for use analyzing counting problems of various kinds that are central to the field.

Factorials & Combinations

Work with factorials, binomial coefficients and related concepts.

Do computations with factorials:

Compute binomial coefficients (combinations):

Compute a multinomial coefficient:

Evaluate a double factorial binomial coefficient:

Integer Partitions

Compute or count the partitions of an integer. Add constraints, specifying the number of parts or part size.

Compute the partitions of an integer:

Specify a constraint on the number of parts:

Restrict to partitions into distinct parts:

Compute the number of partitions:

Combinatorial Functions

Learn about and do computations with combinatorial functions.

Compute a Bernoulli number:

Compute a Stirling number:

Compute a Frobenius number:

Compute Catalan numbers:

Compute Clebsch–Gordan coefficients:

Compute Wigner coefficients:


Compute, count or do algebra with permutations of a set.

Compute the permutations of a set:

Count permutations:

Do algebra with permutations:

More examples

Integer Compositions

Compute or count the compositions of an integer. Put constraints, specifying the number of parts or part size.

Compute the compositions of an integer:

Specify a constraint on the parts:

Latin Squares

Get information about, compute or count Latin squares.

Get information about Latin squares:

Compute the number of Latin squares of a specified size:

Count normalized Latin squares:

Compute bounds on the number of large-size Latin squares:


Step-by-Step Solutions for Discrete Mathematics


  • Graph Theory
  • Integers
  • Logic & Set Theory
  • Probability
  • Enumeration Problems

    Solve a large variety of enumeration problems (also known as counting problems).

    Count the number of possible colored bracelets:

    Count the number of possible fixed necklaces:

    Count Lyndon words: