Minus the registration fee, which is relatively small (like, $500 a year or so), and affordable to all but the most poor (who'd get a scholarship anyway if they really wanted to get in), it is entirely based on grades. We have final exams in secondary school, and based on your grades, you are awarded points. You need a certain number of points to get into a course - the number is determined by demand for the course. You can't buy, or charm your way ahead of other people. There are no interviews, where you can schmooze the college president and drop names. You are pretty much completely anonymous until you are selected. Indeed, the whole distribution of places is handled by one independent authority.
You have 200 faculties per university? Just to be sure we mean the same thing..a faculty is a department within the college, right? My college has like, 10 or so faculties. I based my calculation on 10 faculties per college, and didn't count the per-student costs since we didn't talk about them before

I also took a "few hundred" to mean about 4 hundred (800 would be more like "several" hundred

). Why would one student cost 10k a year? FYI, our government doesn't pay for books etc. etc.