late 14c., permuten, "to change one for another, to interchange," from Old French permuter and directly from Latin permutare "to change thoroughly," from per "thoroughly" (see per) + mutare "to change" (from PIE root *mei- (1) "to change, go, move"). The mathematical sense is from 1878 (see permutation).
late 14c., permutacioun, "interchange, concurrent change; exchange of one thing, position, condition, etc., for another," from Old French permutacion "change, shift" (14c.), from Latin permutationem (nominative permutatio) "a change, alteration, revolution," noun of action from past participle stem of permutare "change thoroughly, exchange," from per "thoroughly" (see per) + mutare "to change" (from PIE root *mei- (1) "to change, go, move"). The sense of "a linear arrangement of objects resulting from a change of their order" is by 1710, originally in mathematics.
Permutation differs from combination in this, that in the latter there is no reference to the order in which the quantities are combined, whereas in the former this order is considered, and consequently the number of permutations always exceeds the number of combinations. [Century Dictionary]
late 14c., from Old French transmutacion "transformation, change, metamorphosis" (12c.), from Late Latin transmutationem (nominative transmutatio) "a change, shift," noun of action from past-participle stem of Latin transmutare "change from one condition to another," from trans "across, beyond; thoroughly" (see trans-) + mutare "to change" (from PIE root *mei- (1) "to change, go, move"). A word from alchemy.
mid-14c., "change the form of" (transitive), from Old French transformer (14c.), from Latin transformare "change in shape, metamorphose," from trans "across, beyond" (see trans-) + formare "to form" (see form (v.)). Intransitive sense "undergo a change of form" is from 1590s. Related: Transformed; transforming.
unit of intensity of pain, 1947, from Latin dolor "pain, grief, sorrow," perhaps from PIE root *delh- "to chop" "under the assumption than 'pain' was expressed by the feeling of 'being torn apart'" [de Vaan].