push out vs show someone the door

push out

verb
  • To force (someone) to leave a group. 

  • To extrude. 

noun
  • In nine ball pool, an optional shot after a legal break shot where a player is allowed to hit any ball first, or not any, as well as not hit a rail, and the opponent can choose who shoots the next shot. 

show someone the door

verb
  • To escort someone to the exit of the premises; to expel someone from a room, gathering, etc. 

  • To dismiss, fire, or reject; to exclude someone who was formerly included. 

How often have the words push out and show someone the door occurred in a corpus of books? (source: Google Ngram Viewer )