give someone the boot vs throw out

give someone the boot

verb
  • (idiomatic, Britain, informal) To fire, sack, or eject someone. 

  • Used other than figuratively or idiomatically: see give, the, boot. 

throw out

verb
  • To discard; to dispense with something; to throw away. 

  • To offer an idea for consideration. 

  • To dismiss or expel someone from any longer performing duty or attending somewhere. 

  • To produce in a haphazard fashion. 

  • To emit. 

  • To cause or experience debilitating muscle or joint pain in (a body part). 

  • To put into a state of confusion. 

  • To cause to project. 

  • To utter carelessly. 

  • To outdistance; to leave behind. 

How often have the words give someone the boot and throw out occurred in a corpus of books? (source: Google Ngram Viewer )