Trina is trying to decide which lunch combination to order at a sandwich shop: 4,5,6, or 7. Each combination comes with the choice of an apple, an orange, or a pear. How many possible outcomes are there for a lunch combination and a piece of fruit?
The Correct Answer and Explanation is :
To determine the total number of possible lunch combinations Trina can order, we need to consider both the sandwich combinations and the fruit choices available.
Step 1: Count the Sandwich Combinations
Trina has four sandwich combinations to choose from: 4, 5, 6, or 7. Therefore, there are 4 possible sandwich choices.
Step 2: Count the Fruit Choices
Each sandwich combination comes with a choice of one fruit: an apple, an orange, or a pear. This provides 3 fruit options.
Step 3: Calculate the Total Number of Combinations
To find the total number of possible lunch combinations, we multiply the number of sandwich choices by the number of fruit choices:
4 (sandwich choices) × 3 (fruit choices) = 12 possible lunch combinations.
Understanding the Multiplication Rule
This calculation is based on the multiplication rule for counting, which states that if one event can occur in m ways and a second event can occur independently of the first in n ways, then the two events can occur in m × n ways. citeturn0search3
Example:
If Trina were to list all possible combinations, they would be:
- Sandwich 4 with Apple
- Sandwich 4 with Orange
- Sandwich 4 with Pear
- Sandwich 5 with Apple
- Sandwich 5 with Orange
- Sandwich 5 with Pear
- Sandwich 6 with Apple
- Sandwich 6 with Orange
- Sandwich 6 with Pear
- Sandwich 7 with Apple
- Sandwich 7 with Orange
- Sandwich 7 with Pear
This list confirms that there are indeed 12 unique lunch combinations.
Conclusion
By applying the multiplication rule, we determine that Trina has 12 possible lunch combinations to choose from, each consisting of one sandwich and one fruit.