by a piece of luck vs fortuitously

by a piece of luck

fortuitously

adv
  • In a fortuitous manner; in a manner of happening by chance; coincidentally; accidentally. 

  • In a fortuitous manner; in a manner of happening by a lucky chance; luckily; fortunately. 

How often have the words by a piece of luck and fortuitously occurred in a corpus of books? (source: Google Ngram Viewer )