displace vs show someone the door

displace

verb
  • To move something, or someone, especially to forcibly move people from their homeland. 

  • To put out of place; to disarrange. 

  • To repress. 

  • To have a weight equal to that of the water displaced. 

  • To replace, on account of being superior to or more suitable than that which is being replaced. 

  • To supplant, or take the place of something or someone; to substitute. 

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 displace and show someone the door occurred in a corpus of books? (source: Google Ngram Viewer )