'permutation' originates from Latin, specifically the word 'permutatio' (from 'permutare'), where 'per-' meant 'thoroughly' and 'mutare' meant 'to change'.

'permutation' changed from Late Latin 'permutatio' and Old French 'permutacion', then into Middle English 'permutacioun', eventually becoming the modern English word 'permutation'.

Initially it meant 'the act of changing thoroughly', but over time it evolved into its current meanings of 'a rearrangement' and, more specifically, the mathematical sense 'an ordered arrangement'.