Math Problem- The Sandwich Shop?

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: Monterrey jack, cheddar, swiss, and american. You can also have mustard, mayonnaise, both or neither. The patrons also get to choose white, wheat, or rye bread, but rye is not offered with t either pastrami or cheddar, as one of the owners objects under the rationale 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?