exceed vs fit the bill

exceed

verb
  • To predominate. 

  • To go beyond (some limit); to surpass; to be longer than. 

  • To be better than (something). 

  • To be larger, greater than (something). 

  • Your password cannot exceed eight characters. 

fit the bill

verb
  • To satisfy a need; to serve a purpose; to fulfill specified requirements. 

How often have the words exceed and fit the bill occurred in a corpus of books? (source: Google Ngram Viewer )