Californiarepoman, I, personally, can't answer your question, but found this video on You TUbe that pertains to your specific question. It is a lecture that covers random graphs and the probablistic method. There might be something in that video that may help you. You have to listen carefully, though, since his English isn't the best. I hope this helps.
Here's the link: Mod-06 Lec-35 Random graphs and probabilistic method: Preliminaries - YouTube
Sorry, that's the best I can do.