Podcast
Questions and Answers
What is the general formula for permutations with repetition?
What is the general formula for permutations with repetition?
- P(n,r)rep = P(n,r) * (x1! * x2! * ... * xo!)
- P(n,r)rep = P(n,r) / (x1! * x2! * ... * xo!) (correct)
- P(n,r) = (n-r)! / n!
- P(n,r) = n! / (n-r)!
What is the value of n in the example of the word 'DIFFERENT'?
What is the value of n in the example of the word 'DIFFERENT'?
- 7
- 2
- 9 (correct)
- 15
What is the value of r in the example of picking 3 balls from a 15-ball pool?
What is the value of r in the example of picking 3 balls from a 15-ball pool?
- 3 (correct)
- 12
- 15
- 2,730
How many arrangements are possible when picking 3 balls from a 15-ball pool?
How many arrangements are possible when picking 3 balls from a 15-ball pool?
In the example with Maria's vases and candle stands, how many items does she have in total?
In the example with Maria's vases and candle stands, how many items does she have in total?
What is the value of x2 in the example with Maria's vases and candle stands?
What is the value of x2 in the example with Maria's vases and candle stands?
What is the value of P(n,r)rep in the example with Maria's vases and candle stands?
What is the value of P(n,r)rep in the example with Maria's vases and candle stands?
What is the formula for calculating the number of circular permutations when the clockwise and counterclockwise arrangements are distinguishable?
What is the formula for calculating the number of circular permutations when the clockwise and counterclockwise arrangements are distinguishable?
In the context of circular permutations, what does 'n' represent?
In the context of circular permutations, what does 'n' represent?
How many different ways can 5 people be arranged in a row?
How many different ways can 5 people be arranged in a row?
How many ways can 6 people be arranged around a circular table where the direction of the arrangement is distinguishable?
How many ways can 6 people be arranged around a circular table where the direction of the arrangement is distinguishable?
In how many ways can the letters of the word 'CHAOS' be arranged?
In how many ways can the letters of the word 'CHAOS' be arranged?
A necklace is made with 8 beads. How many possible arrangements are there if the direction of the arrangement does not matter?
A necklace is made with 8 beads. How many possible arrangements are there if the direction of the arrangement does not matter?
How many different 2-digit numbers can be formed using the digits 1, 2, 3, 4, and 5?
How many different 2-digit numbers can be formed using the digits 1, 2, 3, 4, and 5?
How many ways can you arrange the letters in the word 'LOVE' to form 2-letter words?
How many ways can you arrange the letters in the word 'LOVE' to form 2-letter words?
How many unique 3-digit codes can be created using the digits 1, 2, 3, 4, and 5, if repetitions are allowed?
How many unique 3-digit codes can be created using the digits 1, 2, 3, 4, and 5, if repetitions are allowed?
In how many ways can 10 students be ranked if only the top 3 positions are awarded?
In how many ways can 10 students be ranked if only the top 3 positions are awarded?
Francis needs to select 5 numbers for his password. If he cannot repeat digits, how many different password arrangements can Francis choose?
Francis needs to select 5 numbers for his password. If he cannot repeat digits, how many different password arrangements can Francis choose?
If Carl and Ian want to sit next to each other, how many arrangements are possible if there are 9 people sitting in a row?
If Carl and Ian want to sit next to each other, how many arrangements are possible if there are 9 people sitting in a row?
Calculate the value of P(7, 6).
Calculate the value of P(7, 6).
What is the value of P(5, 2)?
What is the value of P(5, 2)?
If a circular permutation has 5 elements and the clockwise and counter-clockwise arrangements can be distinguished, how many total arrangements are possible?
If a circular permutation has 5 elements and the clockwise and counter-clockwise arrangements can be distinguished, how many total arrangements are possible?
What is the total number of possible outfits that Maria can wear, based on the information provided in the 'Let's Recall' section?
What is the total number of possible outfits that Maria can wear, based on the information provided in the 'Let's Recall' section?
How many different ways can you arrange the letters in the word 'MATHEMATICS'?
How many different ways can you arrange the letters in the word 'MATHEMATICS'?
What is the correct formula for calculating the number of permutations when repeating objects?
What is the correct formula for calculating the number of permutations when repeating objects?
What is the number of possible ways to arrange the letters of the word 'SCHOOL'?
What is the number of possible ways to arrange the letters of the word 'SCHOOL'?
How many different ways are there to choose 3 balls from a pool of 15 balls, if the order of selection does not matter?
How many different ways are there to choose 3 balls from a pool of 15 balls, if the order of selection does not matter?
How many different seating arrangements are possible if 12 country representatives need to be seated in a circular arrangement?
How many different seating arrangements are possible if 12 country representatives need to be seated in a circular arrangement?
How many different 7-digit integers can be formed using the digits 5, 6, 7, and 4?
How many different 7-digit integers can be formed using the digits 5, 6, 7, and 4?
In how many ways can the letters of the word REFERENCE be arranged?
In how many ways can the letters of the word REFERENCE be arranged?
In how many ways can the letters of the word MATHEMATICS be arranged?
In how many ways can the letters of the word MATHEMATICS be arranged?
If there are 3 seats available at a bar, how many ways are there to seat a mathematician, a physicist, and an engineer?
If there are 3 seats available at a bar, how many ways are there to seat a mathematician, a physicist, and an engineer?
Consider a circular table. If a mathematician, physicist, engineer, and computer scientist sit in a specific order at the table, how many different seating arrangements at a bar would lead to this specific order at the table?
Consider a circular table. If a mathematician, physicist, engineer, and computer scientist sit in a specific order at the table, how many different seating arrangements at a bar would lead to this specific order at the table?
Six friends want to form a club with one president, one secretary, and four ordinary members. How many ways can they organize this club?
Six friends want to form a club with one president, one secretary, and four ordinary members. How many ways can they organize this club?
Five children are playing hide-and-seek. Each child hides in a different room out of 7 available rooms. How many ways can the children hide?
Five children are playing hide-and-seek. Each child hides in a different room out of 7 available rooms. How many ways can the children hide?
What is the primary purpose of this module?
What is the primary purpose of this module?
What is the main objective of this module?
What is the main objective of this module?
Who is the target audience for this module?
Who is the target audience for this module?
Which of the following best describes the module's approach to learning?
Which of the following best describes the module's approach to learning?
What is the role of the facilitator in using this module?
What is the role of the facilitator in using this module?
Which of the following is NOT a reminder given to learners using this module?
Which of the following is NOT a reminder given to learners using this module?
What is the purpose of the "Let's Try" section of the module?
What is the purpose of the "Let's Try" section of the module?
What is the significance of the phrase "you can do it!" in the module?
What is the significance of the phrase "you can do it!" in the module?
Flashcards
Permutation Formula
Permutation Formula
The formula for permutations is n! / (n - r)!
Example of Permutation
Example of Permutation
Selecting 3 balls from a pool of 15 results in 2,730 arrangements.
Permutations with Repetition
Permutations with Repetition
Total permutations divided by the factorial of identical elements.
DIFFERENT Word Permutation
DIFFERENT Word Permutation
Signup and view all the flashcards
Total Letters in DIFFERENT
Total Letters in DIFFERENT
Signup and view all the flashcards
Arrangement of Homogeneous Items
Arrangement of Homogeneous Items
Signup and view all the flashcards
Use of Factorial
Use of Factorial
Signup and view all the flashcards
Cancellation in Permutation
Cancellation in Permutation
Signup and view all the flashcards
Module Purpose
Module Purpose
Signup and view all the flashcards
Active Learning
Active Learning
Signup and view all the flashcards
Permutation
Permutation
Signup and view all the flashcards
Formula for Permutation
Formula for Permutation
Signup and view all the flashcards
Task Instructions
Task Instructions
Signup and view all the flashcards
Integrity in Tasks
Integrity in Tasks
Signup and view all the flashcards
Returning the Module
Returning the Module
Signup and view all the flashcards
Task Completion
Task Completion
Signup and view all the flashcards
Circular Permutation
Circular Permutation
Signup and view all the flashcards
Distinguishable Circular Permutation
Distinguishable Circular Permutation
Signup and view all the flashcards
Indistinguishable Circular Permutation
Indistinguishable Circular Permutation
Signup and view all the flashcards
Formula for Distinguishable Circular Permutation
Formula for Distinguishable Circular Permutation
Signup and view all the flashcards
Formula for Indistinguishable Circular Permutation
Formula for Indistinguishable Circular Permutation
Signup and view all the flashcards
Arrangement of 10 persons
Arrangement of 10 persons
Signup and view all the flashcards
Arrangement of 7 diamonds
Arrangement of 7 diamonds
Signup and view all the flashcards
Outfit Combinations
Outfit Combinations
Signup and view all the flashcards
Blouse Types
Blouse Types
Signup and view all the flashcards
Skirt Colors
Skirt Colors
Signup and view all the flashcards
Counting Pairs
Counting Pairs
Signup and view all the flashcards
Total Combinations Formula
Total Combinations Formula
Signup and view all the flashcards
Permutation without repetition
Permutation without repetition
Signup and view all the flashcards
Distinct circular permutation (clockwise)
Distinct circular permutation (clockwise)
Signup and view all the flashcards
Identical elements in permutations
Identical elements in permutations
Signup and view all the flashcards
3-digit codes unique with repetition
3-digit codes unique with repetition
Signup and view all the flashcards
Arrangements of a password
Arrangements of a password
Signup and view all the flashcards
Circular seating arrangements
Circular seating arrangements
Signup and view all the flashcards
Arranging digits
Arranging digits
Signup and view all the flashcards
Word arrangements with repetitions
Word arrangements with repetitions
Signup and view all the flashcards
Seating arrangements for distinct individuals
Seating arrangements for distinct individuals
Signup and view all the flashcards
Ways to select positions
Ways to select positions
Signup and view all the flashcards
Hide-and-seek arrangements
Hide-and-seek arrangements
Signup and view all the flashcards
Total arrangements formula
Total arrangements formula
Signup and view all the flashcards
Factorial notation
Factorial notation
Signup and view all the flashcards
Study Notes
Mathematics Third Quarter Module 1, Week 1
- Module Purpose: To help learners meet K-12 curriculum standards and overcome personal, social, and economic constraints in schooling.
- Learner Instructions:
- Use the module carefully, using a separate sheet for exercises.
- Answer "Let's Try" before proceeding to other activities.
- Read instructions carefully before each task.
- Maintain honesty and integrity.
- Complete one task before moving on to the next.
- Return the module to the teacher/facilitator when finished.
- Seek help from the teacher/facilitator if needed.
- Facilitation Responsibilities:
- Guide learners through the module.
- Monitor learner progress.
- Encourage and assist learners with tasks.
- Orient learners on how to use the Module.
- Topic Focus: Permutation of objects, listing possible ways to perform tasks, and applying the permutation formula for n objects taken r at a time.
- Permutation Formula: P(n,r) = n! / (n-r)!
- Factorial Notation: n! = n × (n-1) × (n-2) ... × 2 × 1
- Fundamental Counting Principle: If one action can occur in 'a' ways and a second action in 'b' ways, both actions can be accomplished in 'a × b' ways. This holds only if the choices are independent.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
This module focuses on permutations of objects, teaching students how to list possible arrangements and apply the permutation formula for selecting r objects from n total. Tailored for the K-12 curriculum, it provides structured activities to guide learners through each task effectively. Complete the exercises with integrity and accuracy to enhance your understanding of permutations.
