Why do you say that?
I'm confused. You said, "...57 difficult homework questions in a week that he's not even going to grade...", but then you said, "...a tight deadline assignment and then randomly choosing what you're going to grade..."
Which is it? Is he not going to grade them, or is he going to randomly select some of them to grade?
Only grading some them randomly seems lazy and not conducive to learning (how do you know if/what you got wrong?)
Regarding the 57 hard questions, you said he won't grade them but you'll get 0 if you don't do them (I assume 0 for the course). So just "do" them. You don't have to worry about getting them right. Just make it look like you tried. You can get them all wrong and it won't matter. From the sound of it, I doubt if the prof will even look at them, they will just check off the assignment as being "done".
If you want to actually learn the material, you can always go back later and look them over and study them at your leisure.
@Pat For this assignment he grades none, for the rest it's randomly selected.