Math Problem Statement

For $3.98 you can get a salad, main course, and dessert at the cafeteria. If you have a choice of 5 different salads, 2 different main courses, and 6 different desserts, then how many different meals can you get for $3.98?

Solution

The question in the image asks how many different meal combinations you can get for $3.98, given the following choices:

  • 5 different salads
  • 2 different main courses
  • 6 different desserts

To calculate the total number of different meal combinations, you simply multiply the number of choices for each course together.

Total combinations=(number of salads)×(number of main courses)×(number of desserts)\text{Total combinations} = (\text{number of salads}) \times (\text{number of main courses}) \times (\text{number of desserts})

Substituting the values:

Total combinations=5×2×6=60\text{Total combinations} = 5 \times 2 \times 6 = 60

Thus, you can get 60 different meal combinations for $3.98.

Would you like further details or clarifications?

Here are five related questions:

  1. What would happen if you added another category like beverages?
  2. How would the number of combinations change if more options were added for main courses?
  3. If each combination had a different probability of being selected, how could we calculate the probability of each meal?
  4. How does this problem relate to the concept of permutations versus combinations?
  5. How would limiting the number of salads or desserts to one per customer affect the outcome?

Tip: In these types of problems, always check if the order of choices matters—here it doesn't, as any salad-main-dessert combination is a valid meal.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Multiplication Principle

Formulas

Total combinations = (number of salads) × (number of main courses) × (number of desserts)

Theorems

Fundamental Principle of Counting

Suitable Grade Level

Grades 5-7