Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

4. Probability

Fundamental Counting Principle

Statistics

4. Probability

Fundamental Counting Principle

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1:21 minutes

Problem 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 entrées, and 8 desserts. How many different meals are available when you select an appetizer, an entrée, and a dessert?

Verified step by step guidance

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 entrées, and 8 desserts.

Step 3: Multiply the number of choices for appetizers, entrées, and desserts to find the total number of possible meal combinations. Use the formula:

total = appetizers \times entrées \times desserts

Step 4: Substitute the values into the formula:

total = 6 \times 12 \times 8

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.

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.

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, entrées, and desserts.

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