Probability using combination.
A certain model of remote-control Stanley garage door opener has nine binary (off/on) switches. The homeowner can set any code sequence.
(a) How numerous separate codes can be programmed?
(b) A newer model has 10 binary switches. How many codes can be programmed?
(c) If you try to use your door opener on 1,000 other garages, how many times would you expect to succeed?
What suppositions are you making in your answer?