For example, if you want to study engineering you have to have certain math skills. Otherwise university won't let you in, no matter how much you pay.
Oh, free college no. But tuition is something like $700 annual in germany/france. There is no housing or anything.
Sadly, the quality of education in Czech Republic have degraded significantly in capitalism. We have gotten rid of Marxism-Leninism but have also let significantly more people in and set the incentives to produce a lot of graduates with much less knowledge, with rest of the bulk being thrown out after 2 years so that the university gets maximum state support.
We are probably going to end up with student loans and lower government participation, which will ruin our education system completely.
"the quality of education in Czech Republic have degraded significantly in capitalism... so that the university gets maximum state support."
I wouldn't think 'university gets maximum state support' to be a shining example of (free-market) capitalism. If anything, it sounds exactly like what the original article complains, if only a bit more direct and less sneaky than channeling the mechanism of subsidy through a convoluted, corrupt, and rent-seeking banking system.
Basically you can apply to any university and they will let you in. Sometimes you need maths, but mostly it is open. If you don't score 50 out of 60 credits in your first year you're out. You fail a class if your grades are too low, which is more frequent than would happen in usa.