A permutation counts arrangements where order matters, while a combination counts selections where order doesn’t matter.
Both concepts count ways to select items from a group, but the key question is whether the order of selection changes the outcome.
Arranging 3 books out of 5 on a shelf — the order matters, because "Book A, then B, then C" is different from "Book C, then A, then B." This uses the permutation formula.
Choosing 3 books out of 5 to take on a trip — you just care which 3 books you end up with, not the order you picked them in. This uses the combination formula, which is always smaller than or equal to the permutation count for the same numbers, since it doesn't count reordered duplicates separately.
Last reviewed: September 2026