All Random? Yeah right.

This is something that I find very frustrating when playing AR URF or ARAM. Every single game. I'm always getting the exact same few handful champions including Yorick, Kayle, Nautilus, and a few others. Even when I reroll, I get another champion of these few and even the SAME CHAMP I HAD BEFORE. I don't think it's due to how many champions I own, because I have most of them. I don't really have anything against these champs, but I think it would be kinda nice to actually get a different champ once in a while. Isn't that kind of the point of all random?