Question

multiple choice
listen
imagine a restaurant that allows you to design your own meal by:

• selecting one of five proteins (beef, poultry, pork, fish, or tofu)
• selecting one of four vegetables (broccoli, corn, cauliflower, or potatoes)
• selecting one of three additional sides (pasta, soup, or garlic bread)

how many total unique dinner options does the restaurant offer if you must choose one protein, one vegetable, and one side?
a 12
b 60
c 240
d 27

Explanation:

Step1: Identify the number of choices for each category

• Proteins: 5 options (beef, poultry, pork, fish, tofu)
• Vegetables: 4 options (broccoli, corn, cauliflower, potatoes)
• Sides: 3 options (pasta, soup, garlic bread)

Step2: Apply the multiplication principle

To find the total number of unique dinner options, we multiply the number of choices for each category together. This is because for each protein, there are multiple vegetable choices, and for each protein-vegetable combination, there are multiple side choices. The formula for the multiplication principle in counting is:

$$ \text{Total options} = \text{Number of protein choices} \times \text{Number of vegetable choices} \times \text{Number of side choices} $$

Substituting the values we have:

$$ \text{Total options} = 5 \times 4 \times 3 $$

Step3: Calculate the result

First, calculate \(5 \times 4 = 20\). Then, multiply that result by 3: \(20 \times 3 = 60\).

Answer:

B. 60