(a) Recall that Kn is the complete graph on n vertices, which is the unique simple graph

on n vertices in which every pair of distinct vertices are neighbors. Find the formula

for |E(Kn)|, the number of edges of Kn, using two different methods. Hint: degrees

and binomial coefficients, for example.

(b) Prove by induction that your formula for |E(Kn)| is correct. Write complete sentences,

use the correct language and format for induction proof, and do not leave out any

details.