re: how big was this particular class.
Columbia College is part of Columbia University. The college only has 4,100 students.
Class of ‘83 political science, pre-law Columbia University — 400 students — that’s why Fox interviewed 400.
Obama’s not in the yearbook. Columbia couldn’t find a picture of him at school.
Wayne Allen Root was BMOC — he knew everyone and everyone knew him.
There's no way there were 400 students in a single major. Until recently, Columbia College had only around 800 students in a graduating class (they increased class size around a 1000 a few years ago).
It seems that they contacted approximately 50% of the graduating class to see whether anyone knew him.
It's quite plausible that, for a student who kept to himself and wasn't very social, more than half his classmates wouldn't know him. That appears to be what happened here.
As to the yearbook, well, I don't remember there being one when I graduated. Maybe they had one in 1983, but if they did, I doubt it was very many people paid much attention to it.
The alumni magazine, however, did publish a photo or two of him from his college days earlier this year.