>I've actually encountered keypads where the order didn't actually matter
If the order really doesn't matter, then that counts combinations twice (1234, 1243..). There are 10000 possible 4-digit codes, 5040 permutations, and actually 210 combinations.
You haven't taken into account that by looking at the keypad you can tell which digits are actually used.
Because from fingerprints and similar gunk on the pad you can tell which 4 digits were used.