Penn accepts students by school, not major. The schools that accept undergraduates are Arts & Sciences (the biggest, basically most of what any other Ivy offers), Wharton (business and finance), Engineering & Applied Science (engineering, architecture, etc.), and Nursing. I think Nursing and Engineering have the highest acceptance rates -- but that's because they don't really draw applications from people who don't know what they want to do; admission is very competitive among the self-selected applicants. Wharton has an ultra-low acceptance rate because it's really, really popular these days as the clear #1 undergraduate business program in, well, the world. Arts & Sciences is sort of normal impossible-to-get-into Ivy.
Prospective freshmen can apply to some formal joint degree programs between Wharton and SAS or SEAS, but they are really hard to get accepted to.
Except for those joint degree programs, officially no one cares what major you might choose within a particular school when you apply. Unofficially they probably try to be certain to admit a class with balanced interests to each school, so Arts & Sciences won't be 50% economics majors and 50% pre-meds, and SEAS won't be all computer science people. But you are not applying to be a Classics major, or a Sociology major, or a Mechanical Engineering major.