Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

4. Probability

Fundamental Counting Principle

Statistics

4. Probability

Fundamental Counting Principle

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2:07 minutes

Problem 3.R.5

Textbook Question

"In Exercises 5 and 6, use the Fundamental Counting Principle.
5. A student must choose from seven classes to take at 8:00 A.M., four classes to take at 9:00 A.M., and three classes to take at 10:00 A.M. How many ways can the student arrange the schedule?"

Verified step by step guidance

Understand the Fundamental Counting Principle: This principle states that if there are multiple events, and each event has a certain number of outcomes, the total number of outcomes is the product of the outcomes for each event.

Identify the events in the problem: The student is choosing one class for each of three time slots: 8:00 A.M., 9:00 A.M., and 10:00 A.M.

Determine the number of choices for each event: The student has 7 choices for the 8:00 A.M. class, 4 choices for the 9:00 A.M. class, and 3 choices for the 10:00 A.M. class.

Apply the Fundamental Counting Principle: Multiply the number of choices for each time slot. This can be expressed as:

7 \times 4 \times 3

Interpret the result: The product of these numbers represents the total number of ways the student can arrange their schedule.

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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 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways to perform both actions. This principle is essential for calculating the total number of combinations or arrangements in scenarios where multiple choices are involved.

Combinations

Combinations refer to the selection of items from a larger set where the order does not matter. In the context of the question, the student is choosing classes, and the specific order of selection is irrelevant, making combinations a key concept for determining the number of possible schedules.

Permutations

Permutations involve the arrangement of items where the order does matter. While the question primarily focuses on combinations, understanding permutations is important for grasping how different arrangements can affect the total count of possible schedules, especially if the order of classes were to be considered.

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Multiple Choice

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"In Exercises 5 and 6, use the Fundamental Counting Principle.5. A student must choose from seven classes to take at 8:00 A.M., four classes to take at 9:00 A.M., and three classes to take at 10:00 A.M. How many ways can the student arrange the schedule?"

Key Concepts

Fundamental Counting Principle

Combinations

Permutations

Watch next

"In Exercises 5 and 6, use the Fundamental Counting Principle.
5. A student must choose from seven classes to take at 8:00 A.M., four classes to take at 9:00 A.M., and three classes to take at 10:00 A.M. How many ways can the student arrange the schedule?"