Several teachers invested together in a sandwich and soda shop. They call it the “Teacher’s Sub Shop.” They offer custom-made sandwiches. You can buy a sandwich with the following bases; pastrami, turkey, roast beef, or vegetarian. Along with that, they offer four kinds of cheese; Monterey Jack, Cheddar, Swiss, American. You can also have mustard, mayonnaise, both or neither. The patrons also get to choose white wheat, or rye bread, but the rye is not offered with either pastrami or cheddar, as one of the owners objects under the rational that the combinations of cheddar and rye or pastrami and rye are “gross.” You also can’t get mustard on turkey or mayonnaise on roast beef. A sandwich consists of one base, one cheese if desired, condiments if desired, and one bread. How many different types of sandwiches exist at this shop? Show Your work.