I don't have any issues with calculation on these problems, but I worry that the semantics of these problems may change how they are meant to be calculated. I've provided the questions and my current answers.
How many bit strings of length 16 contain
a) Exactly 4 more ones than zeros?
b) Exactly 2 ones and 14 zeros?
c) Three times as many ones as zeros?
I can't shake the feeling that the way these questions are worded changes their meaning. Can someone confirm my answers?