Podcast
Questions and Answers
How many ways can a president, a vice president, and a secretary be chosen from Aaron, Blessie, Carmi, Darius, Elvie, and Von?
How many ways can a president, a vice president, and a secretary be chosen from Aaron, Blessie, Carmi, Darius, Elvie, and Von?
If ORDER IS IMPORTANT, how many outcomes are there when choosing 2 gentlemen from Mike, Kevin, Daryl, and Glen?
If ORDER IS IMPORTANT, how many outcomes are there when choosing 2 gentlemen from Mike, Kevin, Daryl, and Glen?
How many ways can a teacher select 4 students from a group of 8?
How many ways can a teacher select 4 students from a group of 8?
In how many ways can a committee of 5 members be formed from a pool of 7 men and 9 women, ensuring there are at least 3 women?
In how many ways can a committee of 5 members be formed from a pool of 7 men and 9 women, ensuring there are at least 3 women?
Signup and view all the answers
How many ways can the coach select a starting lineup of 5 players from a basketball team of 10 players?
How many ways can the coach select a starting lineup of 5 players from a basketball team of 10 players?
Signup and view all the answers
If selecting 2 gentlemen from Mike, Kevin, Daryl, and Glen is a situation where order is NOT important, how many unique outcomes are there?
If selecting 2 gentlemen from Mike, Kevin, Daryl, and Glen is a situation where order is NOT important, how many unique outcomes are there?
Signup and view all the answers
What is the procedure for finding combinations of n objects taken r at a time without creating a diagram?
What is the procedure for finding combinations of n objects taken r at a time without creating a diagram?
Signup and view all the answers
What distinguishes a permutation from a combination?
What distinguishes a permutation from a combination?
Signup and view all the answers
In a science club of 11 boys and 13 girls, how many groups can be formed if exactly 4 boys need to be selected for a group of 6 students?
In a science club of 11 boys and 13 girls, how many groups can be formed if exactly 4 boys need to be selected for a group of 6 students?
Signup and view all the answers
How many elimination games are played in a tournament with 12 teams if each team plays every other team once?
How many elimination games are played in a tournament with 12 teams if each team plays every other team once?
Signup and view all the answers
Study Notes
Permutation of Objects
- Permutation is an arrangement of objects in a specific order.
- The order of selection matters in permutations.
- Examples of scenarios involving permutations include arranging books on a shelf, selecting people for president and vice president of a club or arranging the letters of a word.
Permutation Example
- Find the number of ways a president, vice president, and secretary can be chosen from Aaron, Blessie, Carmi, Darius, Elvie, and Von.
- There are 6 possible choices for president.
- Once a president is chosen, there are 5 remaining choices for vice president.
- Then there are 4 remaining choices for secretary.
- Total ways to choose is 6 × 5 × 4 = 120
Activity: Selecting Two Representatives
- Create a tree diagram to show how two gentlemen from Mike, Kevin, Daryl, and Glen will be chosen for a seminar
- The order in which the selection is made matters in this scenario.
Process Questions
- How many possible outcomes exist if the order is important (e.g., Mike, Kevin is different from Kevin, Mike)?
- To find this, multiply the number of choices each time.
- Calculate the number of selections if the order does not matter. These selections are the same regardless of the order.
- Example: Mike, Kevin is the same as Kevin, Mike.
- How can you calculate the number of selections in the case where order does not matter?
Combinations
- Combinations are selections of items where order does not matter.
- In a combination, the order of selection does not matter.
- An example of a combination could include selecting a group of students from a classroom, where the order of selection doesn't affect the overall group.
Learning Targets
- Illustrate combinations of objects
- Differentiate between permutation and combination
- Real-world examples involving combinations
Combinations of N Objects Taken R at a Time
- How to calculate combinations without diagrams?
Problem Solving
- Basketball Tournament: 12 teams are playing, find the number of elimination games.
- Households: A researcher needs to select 10 households from 30. In how many ways can a sample be selected?
Review
- Tell whether situations (like arranging books, picking team members, or creating a song playlist) are permutations or combinations.
Seatwork
- Students: How many ways can a teacher choose 4 students from 8?
- Committee: Form a committee of 5 members from 7 men and 9 women with at least 3 women.
- Basketball Team: A basketball team has 10 players. How many ways can the coach select a starting lineup of 5 players?
- Science Club: How many groups can be formed if 6 students are selected from 11 boys and 13 girls, and exactly 4 boys are in the group?
Additional Problems
- Committee: Form a committee of 7 members from a selection pool of 15 men and 13 women, with at most 4 women
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
This quiz covers the concept of permutations, including the arrangement of objects in a specific order and scenarios where the order of selection matters. You'll find examples and activities designed to test your understanding of permutations and their applications in decision-making processes.
