arbitrarily vs willy-nilly

arbitrarily and willy-nilly both are adverbs.

Word	Noun	Adjective	Verb	Adverb
arbitrarily	No	No	No	Yes
willy-nilly	No	No	No	Yes

As adverbs, arbitrarily and willy-nilly are synonyms defined as:

Other synonyms of arbitrarily include at random, every which way, haphazardly, indiscriminately, randomly.

arbitrarily (adverb)	willy-nilly (adverb)
in a random manner	in a random manner
	without having a choice