Question

A sandwich shop allows you to choose from italian bread, a whole wheat roll, or a wrap. then you can choose one type of meat: roast beef, turkey, chicken, or ham. finally, you can choose one type of cheese: provolone, swiss, american, or cheddar. which shows how to apply the fundamental counting principle to calculate the number of possible outcomes?

A. 3 × 3 × 3
B. 1 × 1 × 1
C. 3 × 1 × 1
D. 3 × 4 × 4

Answer 1

The number of possible outcomes for creating a sandwich at the shop is calculated using the fundamental counting principle, resulting in 3 types of bread × 4 types of meat × 4 types of cheese, which equals 48 unique combinations.

Step-by-step explanation:

To calculate the number of possible outcomes for the given sandwich shop choices, you apply the fundamental counting principle. This principle states that if you have several categories of items and each category has a certain number of options, you can find the total number of unique combinations by multiplying the number of options in each category.

According to the problem, you have the following categories and options:

• Bread: 3 options (Italian bread, whole wheat roll, wrap)
• Meat: 4 options (roast beef, turkey, chicken, ham)
• Cheese: 4 options (provolone, swiss, american, cheddar)

To find the total number of sandwich combinations, you multiply the number of options in each category:

3 (types of bread) × 4 (types of meat) × 4 (types of cheese) = 48 possible outcomes

Therefore, the correct application of the fundamental counting principle to calculate the number of possible outcomes is represented by option D.