The Princeton application asks you to indicate whether you want to major in Bachelor of Arts or in Bachelor of Science in Engineering, with the BSE applicants having to write an extra supplement. When you indicate either as your choice, are you bound to that school if you get accepted and choose to attend, or can you make the final choice later?
You are admitted to Princeton itself, and can choose between AB or BSE before school starts. You can change your mind freshman year too. It becomes more difficult to switch INTO BSE after the first year because of engineering class requirements.