Podcast
Questions and Answers
Which of the expressions represents the total number of ways to arrange $n$ distinct objects?
Which of the expressions represents the total number of ways to arrange $n$ distinct objects?
- $n + n$
- $2n$
- $n^2$
- $n!$ (correct)
A combination considers the order of elements, while a permutation does not.
A combination considers the order of elements, while a permutation does not.
False (B)
When is it appropriate to use permutations instead of combinations to solve a counting problem?
When is it appropriate to use permutations instead of combinations to solve a counting problem?
when order matters
If two events, A and B, are mutually exclusive, then $P(A \cup B) = P(A) ______ P(B)$.
If two events, A and B, are mutually exclusive, then $P(A \cup B) = P(A) ______ P(B)$.
In probability, what does the intersection of two events, denoted as $A \cap B$, represent?
In probability, what does the intersection of two events, denoted as $A \cap B$, represent?
If events A and B are independent, then $P(A \cap B) = P(A) + P(B)$.
If events A and B are independent, then $P(A \cap B) = P(A) + P(B)$.
What condition must be met for two events to be considered 'mutually exclusive'?
What condition must be met for two events to be considered 'mutually exclusive'?
The formula for calculating permutations, where order matters, is given by $P(n, r) = ______ / (n - r)!$.
The formula for calculating permutations, where order matters, is given by $P(n, r) = ______ / (n - r)!$.
What is the primary difference between a permutation and a combination?
What is the primary difference between a permutation and a combination?
The union of two events always results in a smaller probability than either event individually.
The union of two events always results in a smaller probability than either event individually.
Briefly explain the difference between independent and mutually exclusive events.
Briefly explain the difference between independent and mutually exclusive events.
The formula for combinations, where order does not matter, is given by $C(n, r) = n! / (______ * (n - r)!)$.
The formula for combinations, where order does not matter, is given by $C(n, r) = n! / (______ * (n - r)!)$.
If A and B are mutually exclusive events, which of the following equations is true?
If A and B are mutually exclusive events, which of the following equations is true?
If an event is certain to happen, its probability is 1.
If an event is certain to happen, its probability is 1.
Match the following statistical terms:
Match the following statistical terms:
Flashcards
What is a Permutation?
What is a Permutation?
An arrangement of objects in a specific order.
Permutation Formula
Permutation Formula
A method for computing the number of ways to arrange a set of objects in a particular order.
Combination
Combination
The number of ways to choose a subset of objects from a larger set without regard to order.
What is an event?
What is an event?
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Union of Events
Union of Events
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Intersection of Events
Intersection of Events
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Probability
Probability
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Mutually Exclusive Events
Mutually Exclusive Events
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Probability of A or B
Probability of A or B
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Study Notes
- The Table of Specifications is for Grade 10 Mathematics, 4th Grading Period, SY 2015-2016.
- It details learning competencies, contact hours/days, number of items, and levels of difficulty.
- Total contact hours/days are 25, with a total of 70 items.
Learning Competencies
- Illustrates the permutation of objects, requiring 1 contact hour/day and includes 3 items.
- Derives the formula for finding the number of permutations of n objects taken r at a time, requiring 2 contact hours/days and includes 7 items.
- Solves problems involving permutations, requiring 3 contact hours/days and includes 9 items.
- Illustrates the combination of objects, requiring 1 contact hour/day and includes 3 items.
- Differentiates permutation from combination of n objects taken r at a time, requiring 2 contact hours/days and includes 7 items.
- Derives the formula for finding the number of permutations of n objects taken r at a time, requiring 3 contact hours/days and includes 8 items.
- Solves problems involving permutations and combinations, requiring 3 contact hours/days and includes 8 items.
- Illustrates events, and union and intersection of events, requiring 1 contact hour/day and includes 3 items.
- Illustrates the probability of a union of two events, requiring 1 contact hour/day and includes 3 items.
- Finds the probability of A U B, requiring 3 contact hours/days and includes 8 items.
- Illustrates mutually exclusive events, requiring 1 contact hour/day and includes 3 items.
- Solves problems involving probability, requiring 3 contact hours/days and includes 8 items.
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