This one's pretty easy actually. Since the B class starts prior to the A class and you will supposedly know 2 weeks prior if B will confirm you, there is no problem here. Stay committed to A until you hear from B and give them as much notice as you can with apologies if you're going to B instead.
As for C, go interview and worry about that later if they offer you the job and you still think C might be a better opportunity at that point.
It's a bit of a tough spot for people with integrity, but this business just works this way. Do not feel bad about leaving A or B for C if you choose, just don't expect them to ever give you another shot if things don't work out at C.
Good luck.