Permutation and Combination
Etymology
“Permutation” is from Latin “permutare” (to change thoroughly), per- plus mutare (to change); “combination” from “combinare” (to join two together), com- plus bini (two by two). Both entered mathematics through the study of counting and probability.
noun phrase · /pur-myoo-TAY-shuhn and kom-bih-NAY-shuhn/
Two ways of counting selections: permutations count arrangements where order matters, combinations where it does not.
What it names
It pins down a distinction people blur constantly — a “combination lock” is really a permutation lock.
Example
Three runners can finish in 6 permutations (order matters for the podium) but form only 1 combination if you just ask which three ran.
Related idea
The two rely on factorial arithmetic and answer different questions; using a permutation count where a combination is meant over-counts every result by the number of ways its members could be reordered.