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Questions and Answers
At the end of the lesson, students should be able to illustrate the Fundamental Principles of ______
At the end of the lesson, students should be able to illustrate the Fundamental Principles of ______
Counting
The multiplication rule is used to solve word problems by using ______
The multiplication rule is used to solve word problems by using ______
multiplication
Probability helps to decide about the certainty or uncertainty of a certain ______ under consideration
Probability helps to decide about the certainty or uncertainty of a certain ______ under consideration
event
Consider the following experiments like flipping a coin, tossing a die, and playing a deck of ______
Consider the following experiments like flipping a coin, tossing a die, and playing a deck of ______
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How many different three-letter words can be formed without repetition of ______?
How many different three-letter words can be formed without repetition of ______?
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In the first blank space, there are three candidates, say , a, b and ______
In the first blank space, there are three candidates, say , a, b and ______
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If one of the three letters is positioned already in the first blank space, the second blank space would be for the remaining two letters and there are two possible ways to do it. Lastly, the last blank space would be for the last letter and this can be done in ______ way.
If one of the three letters is positioned already in the first blank space, the second blank space would be for the remaining two letters and there are two possible ways to do it. Lastly, the last blank space would be for the last letter and this can be done in ______ way.
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Hence, there are 3 x 2 x 1 = ______ ways of forming a three-letter word without repetition.
Hence, there are 3 x 2 x 1 = ______ ways of forming a three-letter word without repetition.
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An exam contains five 'true or false' questions. In how many different ways can the exam be completed? Solution: This problem can be solved using spaces that would represent the way of answering a true or false type of questions. Say, for number 1, we can answer it in two ways, that is, 1. T F 2 ways 2. T F 2 ways 5. T F 2 ways Hence, we have 2 x 2 x 2 x 2 x 2 = ______ ways of answering a five true or false type of questions.
An exam contains five 'true or false' questions. In how many different ways can the exam be completed? Solution: This problem can be solved using spaces that would represent the way of answering a true or false type of questions. Say, for number 1, we can answer it in two ways, that is, 1. T F 2 ways 2. T F 2 ways 5. T F 2 ways Hence, we have 2 x 2 x 2 x 2 x 2 = ______ ways of answering a five true or false type of questions.
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You can watch this video to learn the topic on Fundamental Principles of Counting Statistical significance of experiment | Probability and Statistics | Kha… ______
You can watch this video to learn the topic on Fundamental Principles of Counting Statistical significance of experiment | Probability and Statistics | Kha… ______
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Study Notes
Fundamental Principles of Counting
- The fundamental principles of counting help us decide about the certainty or uncertainty of a certain event under consideration.
- The principle is used to solve problems involving counting and arranging objects in different ways.
Multiplication Rule
- If n tasks are to be done, and each task can be accomplished in a certain number of ways, then the total number of possible ways to accomplish all tasks is the product of the number of ways each task can be done.
- Formula: m1 × m2 × m3 × … × mn
Sample Problem 1: Three-Letter Words
- The problem: How many different three-letter words can be formed without repetition of letters?
- Solution: 3 × 2 × 1 = 6 ways, because there are 3 choices for the first letter, 2 choices for the second letter, and 1 choice for the third letter.
Sample Problem 2: True or False Exam
- The problem: In how many different ways can a five-question true or false exam be completed?
- Solution: 2 × 2 × 2 × 2 × 2 = 32 ways, because each question can be answered in 2 ways (true or false).
Importance of Studying Probability
- Probability helps us understand the uncertainty or certainty of an event.
- It is essential in making informed decisions and drawing meaningful conclusions from experiments.
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Description
This quiz covers the Fundamental Principles of Counting, including using the multiplication rule to solve word problems, studying probability, and understanding experiments, outcomes, and events. Test your knowledge on these important concepts!
