'arbitrarily-formed' originates from the word 'arbitrary,' which comes from Latin, specifically the word 'arbitrarius,' where 'arbitr-' meant 'judge or witness.'

'arbitrarius' transformed into the Old French word 'arbitraire,' and eventually became the modern English word 'arbitrary,' which is part of 'arbitrarily-formed.'

Initially, 'arbitrary' meant 'dependent on the will or judgment of a judge,' but over time it evolved into its current meaning of 'based on random choice or personal whim.'