A complete graph on n vertices is randomly edgecoloured with each edge equally likely and independently red or blue with probability 12 A copy of Kk,k la \"complete bipartite graph with vertex sets of sizes k and k\") is any two disjoint subsets; oi k vertices each and all edges ioining all of the vertices in the first subset with all of the vertices in the second subset. This question asks you to find an upper bound for the probability that there is a monochromatic Kk,k- O O The linked tigure illustrates a red K33. . O O k 0 a) Explain why there are 12 ( k k 3,146) ways to pick out two disjoint subsets of k vertices. b) Show that the probability that there is a red Kk,k is at most n2kl2kz . c) Show that if n