How can the sha1sum function give you a unique hash?

I read that using the sha1sum command will run the SHA-1 algorithm and give you a "unique" result, but how can that be? sha1sum gives you a 40 character hash, like this: e5fa44f2b31c1fb553b6021e7360d07d5d91ff5e This is 40 characters long, and has hexadecimal characters, so the hash can have at most 1640 combinations. This should mean that, for any two random files, there *is* a small chance that their hash sum would be exactly the same, right?