Not that I’m reveling in your daughter’s angst, but it’s gratifying to see how well the English and History departments are doing at UCLA as they graduated over 300 majors each last year.
Instinctively, I prefer option A as there’s usually a good option available if your first choice falls through. However, at UW, Applied Computing and Math Sciences, the I-school, statistics and pure math are also competitive with the same group of kids applying. Risk averse students/weaker students interested in quantitative fields only have access to physics as a sure thing. While I don’t know how many people get shutout, I suspect there are a decent number who do especially if they don’t plan really carefully to intersect prerequisities so they’re eligible for multiple majors. Writing this, I realized that wise advising and a willingness to not close any doors (ala Alex Wissner-Gross’ “Intelligence is a Force that Maximises the Future Freedom of Action”) is critical in this environment.
Listing for UW: http://www.washington.edu/uaa/advising/academic-planning/majors-and-minors/list-of-undergraduate-majors/