<p>My friends at private and public (small) schools had to apply for their major before getting admitted, and it was very rare to be able to change, because of the extremely limited teaching resources. The schools also aimed to keep a good male/female balance. They had 0 choice as to classes their first year, their schedules were made for them along with the rest of the freshman class. UVA is not perfect, but I feel very lucky compared to that. You can always major in a hard science within CLAS if you do not do engineering.</p>