Math Problem Statement

Clayton is planning the menu for a dinner party. He wants to serve one main dish, one salad, and one dessert. For the main dish, he can make steak, pasta, or fish. For the salad, Clayton knows how to make potato salad, macaroni salad, or fruit salad. The dessert choices are apple crisp and peach cobbler. How many different menu combinations can Clayton serve?

Solution

To solve this problem, we calculate the total number of menu combinations by multiplying the number of choices for each course (main dish, salad, and dessert). Here's the breakdown:

  1. Main dishes: Steak, Pasta, or Fish = 3 options
  2. Salads: Potato Salad, Macaroni Salad, or Fruit Salad = 3 options
  3. Desserts: Apple Crisp or Peach Cobbler = 2 options

The total number of combinations is:

Total combinations=(Main dishes)×(Salads)×(Desserts)\text{Total combinations} = (\text{Main dishes}) \times (\text{Salads}) \times (\text{Desserts})

Substituting the numbers:

Total combinations=3×3×2=18\text{Total combinations} = 3 \times 3 \times 2 = 18

Final Answer: 18 combinations

Would you like a step-by-step explanation or further clarification?


Here are 5 related questions to explore:

  1. If Clayton adds a fourth main dish option (e.g., chicken), how many total combinations will there be?
  2. What if Clayton eliminates one salad choice—how does this change the total number of combinations?
  3. If he adds a new dessert option, how does it affect the total?
  4. How many combinations are possible if Clayton only serves two courses (main dish and salad)?
  5. Can you create a list of all possible combinations for the current menu?

Tip: Use multiplication to calculate the total combinations in scenarios involving independent choices!

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Multiplication Principle of Counting

Formulas

Total combinations = (Main dishes) × (Salads) × (Desserts)

Theorems

Fundamental Principle of Counting

Suitable Grade Level

Grade 6-8