no vs problem

no

noun
  • a negating expression; an answer that shows disagreement, denial, refusal, or disapproval 

  • a vote not in favor, or opposing a proposition 

det
  • Not any. 

  • Hardly any. 

  • Not (a); not properly, not really; not fully. 

  • Not any possibility or allowance of (doing something). 

prep
  • not, does not, do not, etc. 

  • without 

  • like 

adv
  • Used before different, before comparatives with more and less, and idiomatically before other comparatives. 

  • not 

  • Used idiomatically before certain other adjectives. 

particle
  • Used to show disagreement, negation, denial, refusal, or prohibition. 

  • Used together with an affirmative word or phrase to show agreement. 

  • Used to show agreement with a negative question. 

intj
  • vehement rejection of truthfulness 

  • disgust 

  • mild disapproval 

problem

noun
  • Difficulty in accepting or understanding or refusal to accept or understand. 

  • A difficulty that has to be resolved or dealt with. 

  • A puzzling circumstance. 

  • A set of moves required to complete a climb. 

  • A question to be answered, schoolwork exercise. 

  • Objection. 

adj
  • Causing a problem; problematic; troublesome. 

  • Difficult to train or guide; unruly. 

How often have the words no and problem occurred in a corpus of books? (source: Google Ngram Viewer )