admit vs rule out

admit

verb
  • To be capable of; to permit. In this sense, "of" may be used after the verb, or may be omitted. 

  • To allow to enter; to grant entrance (to), whether into a place, into the mind, or into consideration 

  • To give warrant or allowance, to grant opportunity or permission (+ of). 

  • To allow (someone) to enter a profession or to enjoy a privilege; to recognize as qualified for a franchise. 

  • To concede as true; to acknowledge or assent to, as an allegation which it is impossible to deny (+ to). 

  • To allow to enter a hospital or similar facility for treatment. 

rule out

verb
  • To make unavailable. 

  • To reject an option from a list of possibilities. 

  • To disallow. 

  • To make something impossible. 

  • To cross an item out by drawing a straight line through it, as with a ruler. 

How often have the words admit and rule out occurred in a corpus of books? (source: Google Ngram Viewer )