A certain model of remote-control Stanley garage door opener has six binary (off/on) switches. The homeowner can set any code sequence.
(a) How many separate codes can be programmed?
(b) A newer model has 7 binary switches. How many codes can be programmed?
If you try to use your door opener on 1,300 other garages, how many times would you expect to succeed? (Round answer to 4 decimal places)