Part of going to university is to develop your skills for that career path, but also to make sure you actually want to pursue a career in this field. Personally I went into university as a biology major, but by going through the core curiculum I found I had interests in the more technical fields and thus changed major to biotechnology that enabled be to dive deeper into the areas I enjoyed. Small difference you might say, but some of my classmates made longer jumps from chemistry/physics/medical sciences based on their interests as they proceeded in their studies.
One other thing I will mention, at least from a scientific research standpoint, your ability to experiment will define your career path much more than your degree. For instance, I obtained my PhD in neuroengineering, but now carry out research in biochemistry and DNA sequencing and despite the change in rhematic, the way to carry out research remains universal.