I think this is a question that is important to research school by school. I know some say be true to your interest, however your interests can cross over between many different schools. My D19 is going through this right now. She loves math and that might mean pursuing engineering, in the engineering school, applied math, often in school of letters and science, or even finance, in the business school. When we look at school we try to learn how they evaluate applications. A few we have learned - at UCLA they clearly stated to us that you get considered by the school you apply to, so if she selects engineering, a highly selective school, and does not get selected, she would not be considered for math in the school of letters and science. At UCSB you select a major and alternate. For this campus, if she selects say, electrical engineering, and selects math as a second choice, if she doesn’t get into engineering, she would be considered for the college of letters and science. USC was the most interesting. The application is first read by admissions. They then farm it out to the chosen school. If not selected it goes back to admissions and they might farm it out to the second choice school, or they could admit into the campus undeclared without either of the chosen school choices. At other schools like Stanford, they say students often don’t know what they want so they admit the person, not the school. So there, it doesn’t seem to matter. I just wish this would be more apparent on the website. An important question to ask to college recruiters.