permutation
/ˌpɜːmjʊˈteɪʃ(ə)n/·퍼뮤테이션·noun
a particular ordering of a set of objects; rearrangement
LatinCEFR C1
Root
Latin 'per-' (thoroughly) + 'mutare' (to change)
Latin permutare (to change thoroughly, exchange) → permutatio → English permutation (14th c.)
In a word
Latin per- (thoroughly) + mutare (to change). 'A thorough changing' became 'every rearrangement'. Within the mut family, permutation pushes the quantity of change to the extreme — permutation (every rearrangement), mutation (change), mutate (to change), commute (to exchange). When cryptography and combinatorics call on permutation, a single word turns the Latin verb 'to change' n! times over.
Examples
There are six permutations of three letters.
Cryptography relies on permutations.
Every permutation of the password was tried.
Related
permutepermutationalmutatemutationcommute