In a random graph $G(n,M)$ where $n$ is the number of vertices and $M$ the number of edges, prove that as $n$ tends to infinity $P(G(n,M))=H(n,M))=1$ where $H$ is a graph with $M$ independent edges and $n-2M$ isolated vertices.
This is a problem from Bollobas. I find it intuitively obvious. I tried to do it by calculations but failed.