And just to repeat, many college/university music majors, even at the most selective schools, have no auditions for admission (though there are auditions for extracurricular ensembles). If you do attend a college/university, the presence of a conservatory on campus has pros and cons: most of the best opportunities go to conservatory students. So it can be better sometimes to attend a school that does not have a conservatory. That said, if, say, you entered Oberlin for math and then decided you wanted to do double degree with math and piano, or wanted to do a BM in piano instead of your original math major, you could make that transition.