Why not use a lock with a keycode instead? I don't see a single scenario where Lockitron works better.
http://consumer.schlage.com/Products/Pages/category-landing....
http://consumer.schlage.com/Products/Pages/category-landing....
I had a 4 digit Master lock in 7th grade, and an 8th grader spent a little bit of time with the lock, determined the passcode (chosen at random), and then changed the combination.
I wouldn't put one of these locks on my home, or on anything that I wanted to actually "lock"
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.