'randomly-divided' originates from the combination of 'randomly' and 'divided'. 'Randomly' comes from 'random', which has roots in Old French 'randir', meaning 'to gallop', and 'divided' comes from Latin 'dividere', meaning 'to separate'.

'randomly-divided' evolved from the combination of 'randomly' and 'divided', which were used separately in Middle English and later combined in modern English.

Initially, 'randomly' meant 'without a definite aim', and 'divided' meant 'separated into parts'. The combination retains these meanings in modern usage.