permute (v.)

"through, by means of," 1580s (earlier in various Latin and French phrases, in the latter often par), from Latin per "through, during, by means of, on account of, as in," from PIE root *per- (1) "forward," hence "through, in front of, before, first, chief, toward, near, around, against."

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]