apply to four universities vs apply for college?

Question

I applied to four universities and was accepted by all of them. (http://www.ldoceonline.com/dictionary/apply) Many high school students have begun applying for college. (http://www.learnersdictionary.com/definition/apply)

The two sentences are cited from Webster dictionary and Longman dictionary respectively. I am confused with which preposition (to or for) should I use if I want to say "to request admission to a university". I think "to" is a proper preposition. Why does the second sentence use "to"?

Answer 1

In:

I applied to four universities and was accepted by all of them.

you are applying to a place, so you would use to.

But in:

Many high school students have begun applying for college.

college as used here is the reason you are applying, so here you would use for.

See the definition of apply sense 5:

to make a formal request (to someone for something)

Answer 2

We apply to a school, college, or a university for admission. The use of the preposition "for" in the sentence "Many high school students have begun applying for college" is grammatically incorrect; it should be "........applying to college".