Math Problem Statement

In a restaurant there are 7 starters, 6 main courses and 4 desserts. Levi is going to choose either a starter and a main, a main and a dessert, or a starter, main and dessert. Work out how many possible choices Levi has.

Solution

The question states:

  • There are 7 starters, 6 main courses, and 4 desserts in a restaurant.
  • Levi can choose from two meal options:
    1. A starter and a main.
    2. A starter, a main, and a dessert.

We need to calculate how many possible choices Levi has.


Solution:

1. Choices for "Starter and Main":

  • Number of ways to choose a starter = 7.
  • Number of ways to choose a main = 6.
  • Total combinations for this option = 7×6=427 \times 6 = 42.

2. Choices for "Starter, Main, and Dessert":

  • Number of ways to choose a starter = 7.
  • Number of ways to choose a main = 6.
  • Number of ways to choose a dessert = 4.
  • Total combinations for this option = 7×6×4=1687 \times 6 \times 4 = 168.

3. Total Possible Choices:

Add the results from both options: 42+168=21042 + 168 = 210


Final Answer:

Levi has 210 possible choices.


Do you need further clarification or a detailed breakdown?
Here are five related questions to expand your understanding:

  1. How would the total change if there were 8 starters instead of 7?
  2. What if Levi could also choose only a dessert? How would that affect the total combinations?
  3. How is the total calculated if Levi could select a main course without any other item?
  4. Can we generalize the formula for combinations based on the number of items in each category?
  5. How would adding one more category, such as "beverages," affect the solution?

Tip: When calculating combinations, always check if order matters or if repetition is allowed. Here, order does not matter.

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Math Problem Analysis

Mathematical Concepts

Counting Principles
Combinations and Permutations

Formulas

Total combinations = Product of available choices

Theorems

Fundamental Principle of Counting

Suitable Grade Level

Grades 7-10