Stanley does not clearly distinguish between bijective and double counting proofs, and gives examples of both kinds, but the difference between the two types of combinatorial proof can be seen in an example provided by , of proofs for Cayley's formula stating that there are "n""n" − 2 different trees that can be formed from a given set of "n" nodes. Aigner and Ziegler list four proofs of this theorem, the first of which is bijective and the last of which is a double counting argument. They also mention but do not describe the details of a fifth bijective proof.