4. Probability
Fundamental Counting Principle
1:21 minutesProblem 3.1.37
Textbook Question
Using the Fundamental Counting Principle In Exercises 37-40, use the Fundamental Counting Principle.
37. Menu A restaurant offers a $15 dinner special that lets you choose from 6 appetizers, 12 ±ð²Ô³Ù°ùé±ð²õ, and 8 desserts. How many different meals are available when you select an appetizer, an entrée, and a dessert?
Verified step by step guidance1
Step 1: Understand the Fundamental Counting Principle, which states that if there are multiple choices for different stages of a process, the total number of outcomes is the product of the number of choices at each stage.
Step 2: Identify the choices available for each stage in the problem. Here, the restaurant offers 6 appetizers, 12 ±ð²Ô³Ù°ùé±ð²õ, and 8 desserts.
Step 3: Multiply the number of choices for appetizers, ±ð²Ô³Ù°ùé±ð²õ, and desserts to find the total number of possible meal combinations. Use the formula:
Step 4: Substitute the values into the formula:
Step 5: The result of the multiplication will give the total number of different meals available. Perform the calculation to find the final answer.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Fundamental Counting Principle
The Fundamental Counting Principle states that if there are 'n' ways to do one thing and 'm' ways to do another, then there are n × m ways to perform both actions. This principle is essential for calculating the total number of combinations in scenarios where multiple choices are involved, such as selecting items from a menu.
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Fundamental Counting Principle
Combinations
Combinations refer to the selection of items from a larger set where the order does not matter. In the context of the restaurant menu, each choice of appetizer, entrée, and dessert represents a combination of items that can be selected independently, contributing to the overall meal options.
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Multiplicative Rule
The Multiplicative Rule is a principle in probability and combinatorics that states the total number of outcomes for a series of independent events is the product of the number of outcomes for each event. In this case, the number of meal combinations is calculated by multiplying the number of choices for appetizers, ±ð²Ô³Ù°ùé±ð²õ, and desserts.
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