Cayley's Formula Using The Multinomial Theorem
From the Airport!
I wrote this out on my way to India!
Today, I present to you an interesting problem from the Graph Theory textbook of Bondy and Murty. The topic is Cayley's formula, which gives the number of labelled trees on n vertices. There was a problem in Chapter 4, which gives a hint of using the Multinomial theorem to arrive at a proof of this formula.
The content below is my proof for this theorem using this approach.
The proof below is my original thought process and my work
I hope you enjoyed reading my proof!!!
Credit: Bondy, Adrian, and U S.R. Murty. Graph Theory. Springer, 2008.