Do med students get to pick where they do there residency

Do they apply to the hospitals of their choice, or does their med school assign them to one?

Students apply to a lot of places for residency, get some interviews, and following interviews, students rank their preferences, and the residency programs rank the potential applicants, and then a computer program calculates who goes where based on the rankings from both sides.

The student's medical school doesn't have anything to do with the process, but it isn't a full choice on the student's part either.