Industrial Design/ mechanical engineering in California

Hi everybody! I would like some help with an ideal path choice. I want to become an automotive designer and have been looking into different college paths. By pursuing industrial design, I will be 1 step closer to this goal as well as keep my options open if things don’t work out with my career choice. Currently in California, my options for CAL state colleges are CSULB, SJSU, and SFSU for Industrial design. However, I also want to have a technical background, specifically mechanical engineering. Here are the options I have come up with.

-BS in Industrial design @ SJSU or CSULB and pursue a mechanical engineering grad program
-BS in Industrial design and minor in mechanical engineering at SFSU then pursue a masters in transportation design at Art Center college of design
-BS in mechanical engineering and master in Industrial design

As I said before, I want to keep my career options open aside from automotive design. Please offer your 2 cents on my specific choices or anything related to what I am talking about.

Thanks!