Thread: How many possible combinations in my key lock?

Greetings. I am a woodworker and I design and build very complicated lock systems on my hardwood projects and I am designing a new lock with 15 keyholes. There is one key. The locks are in one line horizontally, and the user does not know that turning the key to the left forces a pin out of a lock sequence or into a lock sequence. The user also doesn't know which position the lock is in when beginning the lock sequence. On the inside of the lockbox, each lock has one pin that either slides in or slides out of a horizontal bar which controls the "real" lock on the lockbox. When all of the pins are in correct position then the box lid can open. The only thing the user will know is there is 1 key and 15 locks. How do I calculate how many possible combinations are there to solving this lock? binomial coefficient, or some type of integer?