an arm and a leg vs worthless

an arm and a leg

noun
  • Usually used after the verb cost, but also often charge, pay, and spend: a very high price for an item or service; an exorbitant price 

worthless

adj
  • Having no worth or use; without value. 

How often have the words an arm and a leg and worthless occurred in a corpus of books? (source: Google Ngram Viewer )