My brain can not let me believe its 100% random, with over 6k total aram games played I can tell you two things,
First, and most importantly free week is going to be more likely to be played due to math, everyone owns it, probability goes up, especially on accounts with low amounts of champions owned.
With that being said, I own around 100 champions, and was blessed with FIRSTROLLED varus 3 times out of 4 games yesterday (check my history numbers may be off by one), which as we all know is mathematically possible, but the odds are getting into lottery stats with multiple back to back same champ rolls.
** TL;DR Within my first 3 games played I can tell you what the entire free week rotation is save for a tank or two due to arams alone.**. And I know the math isn't backing up what I'm seeing.