According to an ad in the newspaper for the local cafe, their Bagel Sandwiches can be "made your way" with "100s of choices for you!" They advertise 7 flavors of bagels, 5 kinds of meat, 3 kinds of cheese, 9 dressings, and 3 veggie selections.
a. If you select a sandwich made with one of each: bagel, meat, cheese, dressing, and veggie (and you don't care about the order), how many different combinations of sandwich do you really have to choose from?
b. Now assume you only eat whole wheat bagels. The same 20 toppings listed above can be used. How many combinations do you have?
c. If you can choose 3 items to go on your bagel, how many different types of sandwiches can you have if the different items are reusable (tomato and double ham would be ok)?
d. If you can choose 3 items but they are not reusable, how many are possible?