If I am not admitted to the BME major does that mean I cannot pursue a career in Biomedical Engineering?

No. Because Biomedical Engineering is very multidisciplinary, there are many paths to a career in this field. Biomedical Engineering is the application of traditional engineering expertise to analyze and solve problems in biology and medicine. This means that you do not have to major in BME to be a Biomedical Engineer. There are a number of bio-related minors and tracks offered by traditional Engineering majors that can prepare students for a career or Graduate School in BME (e.g., Materials Science & Engineering has a Biomaterials track, Mechanical & Aerospace Engineering has a Biomechanics minor, Chemical Engineering has a Biomolecular Engineering Minor). Students who major in one of the more traditional engineering majors will not be at a disadvantage when applying to a Biomedical Engineering graduate program. Furthermore, a significant number of Affiliate Faculty who are primarily appointed in these traditional engineering departments are conducting Biomedical Engineering research. This provides students with the opportunity for undergraduate research in their area of interest even as a non-BME major.