section_path: Methods of proof/Combinatorial proof
section_name: Combinatorial proof
paragraph_text: Combinatorial proof
  
  A combinatorial proof establishes the equivalence of different expressions by showing that they count the same object in different ways. Often a bijection between two sets is used to show that the expressions for their two sizes are equal. Alternatively, a double counting argument provides two different expressions for the size of a single set, again showing that the two expressions are equal.