Possible N plus R question

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I am having trouble with this question on how to solve. Can someone please help?

Mark and Juanita own a sandwich shop. They offer 3 kinds of bread, 5 kinds of meat, and 3 kinds of cheese. Each type of sandwich has a combination of exactly 3 ingredients: 1 bread, 1 meat, and 1 cheese. How many types of sandwiches are possible?

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2 Answers

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When you have multiple independent choices, the total number of options is the product of the number of options at each point. If you think of three flips of a coin, you get two choices at each flip, so $2*2*2$ for all three.

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Applying the combinations for your exercise, first you need to focus on the different kinds of sandwiches. You have 3 of bread, 5 of meat and 3 of cheese. First you pick a bread (from the three), then you pick the meat (from the five), and then the cheese.

Then you need to apply the product rule for these selections.

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