ARURF | Are there certain champs that you will get more of?

I've been playing URF for the past week or so now, and I seem to be getting the same small group of champs every time. Is there a larger chance to get some champs than others? I also see the same champs with the rest of the players too. I mean, take a look at my match history. There is just a small pool of champs. Is anyone else experiencing this, or was this specified by any Riot men. But if anyone is experiencing it or knows anything about it, please say.

Thanks