We use the Fundamental Principle of Counting.

Fundamental Principle of Counting

(problem 1a) Sam is getting dressed and wants to include a belt and a hat. If Sam has three distinct belts and two distinct hats, how many ways can Sam accessorize? Include a tree diagram that illustrates the possibilities.
Sam can accessorize in different ways.
(problem 1b) A couple wants to go on a date. They decide to eat at a restaurant, walk in a park and then see a show. If there are two restaurants that they both like, two nearby parks and two shows playing, how many possibilities are there for their date? Make a tree diagram illustrating the possibilities.
There are different possibilities for their date.
(problem 2a) A three course meal consists of an appetizer, an entree and a dessert. If a restaurant offers a dozen appetizers, a score of entrees and a bakers dozen desserts, how many possible three course meals can be ordered?
The total number of possible three course meals is .
(problem 2b) A sixth grade class of 20 students would like to select a President, Vice-President, Secretary and Treasurer. If no student may serve in more than one post, in how many possible ways can the class officers be selected?
The total number of ways to select the class officers is .
(problem 3) Suppose telephone numbers consist of 7 digits, the first of which cannot be 0 or 1. How many such telephone numbers are possible?
(problem 4) Computer passwords consist of 6 characters, where a character can be either a lower case letter, a digit 1-9, or one of 4 special symbols. How many such passwords are possible?
The number of possible passwords is .
(problem 5) Three 4-sided dice (numbered 1-4), colored red, green and blue, are thrown. The numbers on each die are recorded in the format (red, green, blue). How many outcomes are possible?
The total number of possible outcomes for the three dice in the indicated format is .
(problem 6) How many bit matrices are there?
The number of bit matrices is .