Product and sum rule

1. Product and Sum Rule (12 points) (1) (2 points) There are four major auto routes from Boston to Detroit and six from Detroit to Los Angeles. How many major auto routes are there from Boston to Los Angeles via Detroit? (2) (2 points) How many different three-letter initials with none of the letters repeated can people have? (3) (2 points) How many bit strings are there of length eight? (4) (2 points) How many bit strings are there of length four or less? (5) (2 points) How many bit strings of length n, where n is a positive integer start and end with 1s? (6) (2 points) How many license plates can be made using either three up- percase English letters followed by three digits or four uppercase English letters followed by two digits