Discrete Math:

(12 points) Using the Multiplication and Addition Principles, solve the following count- ing questions. Be sure to explain all your steps, starting with whatever Principles you plan to use. (a) The options available on a particular model of a car are five interior colors, six exterior colors, two types of seats, three types of engines, and three types of radios. How many different possibilities are available to the consumer? b) How many different car license plates can be constructed if the licenses contain three letters followed by two digits with no repeated characters? How many can be constructed if repetitions are allowed? (c) If two dice are rolled, how many outcomes produce a sum of 4 or a sum of 8? (d) Using the characters {A, B, C, D, E, F,G), how many strings of length 5 can be formed that do not begin with AC or D