2. [-/2.5 Points] DETAILS ASWESBE9 4.E.003. MY NOTES How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F. (Enter your answers as a comma-separated list. Enter three unspaced capital letters for each permutation.) Need Help? Read It O Show My Work (Optional) ? What steps or reasoning did you use? Your work may add bonus points towards your score. You can submit show my work an unlimited number of times. Uploaded File (10 file maximum) No Files to Display O Upload File
2. [-/2.5 Points] DETAILS ASWESBE9 4.E.003. MY NOTES How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F. (Enter your answers as a comma-separated list. Enter three unspaced capital letters for each permutation.) Need Help? Read It O Show My Work (Optional) ? What steps or reasoning did you use? Your work may add bonus points towards your score. You can submit show my work an unlimited number of times. Uploaded File (10 file maximum) No Files to Display O Upload File
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Topic Video
Question
Answers only please.
![**Permutations of Three Items from a Group of Six**
To determine how many permutations of three items can be selected from a group of six, follow the steps below. This exercise will help you understand permutations and how to list them systematically.
**Problem Statement**:
How many permutations of three items can be selected from a group of six?
**Instructions**:
1. Use the letters A, B, C, D, E, and F to identify the items.
2. List each of the permutations of items B, D, and F.
3. Enter your answers as a comma-separated list.
4. Enter three unspaced capital letters for each permutation.
**Steps to Solve**:
1. **Identify the number of items and the group size**:
- Total items: 6 (A, B, C, D, E, F)
- Number of items to select: 3
2. **Calculate the permutations**:
- The formula for permutations of selecting \( r \) items from \( n \) items is:
\[
P(n, r) = \frac{n!}{(n-r)!}
\]
- For this problem, \( n = 6 \) and \( r = 3 \):
\[
P(6, 3) = \frac{6!}{(6-3)!} = \frac{6 \times 5 \times 4 \times 3!}{3!} = 6 \times 5 \times 4 = 120
\]
- Thus, there are 120 permutations of choosing 3 items from a group of 6.
3. **List permutations of B, D, and F**:
- For three specific items (B, D, F), generate the permutations:
\[
\text{BDF, BFD, DBF, DFB, FBD, FDB}
\]
These permutations are important in helping understand how arrangements are made in different scenarios, whether in mathematics, computer science, or organizing physical and digital objects.
**Optional Show My Work Section**:
- Use this section to detail the steps and reasoning you used to find the permutations.
- This can help in gaining a better understanding, and may also earn bonus points.
**Need Help?**:
- Click the "Read it" button if you need further assistance or examples on how to solve](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbac5cd56-9885-4a25-8e51-dfc1bb78a29e%2F908b1c05-7415-410d-99ab-3f42d7254da9%2Fst5q7a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Permutations of Three Items from a Group of Six**
To determine how many permutations of three items can be selected from a group of six, follow the steps below. This exercise will help you understand permutations and how to list them systematically.
**Problem Statement**:
How many permutations of three items can be selected from a group of six?
**Instructions**:
1. Use the letters A, B, C, D, E, and F to identify the items.
2. List each of the permutations of items B, D, and F.
3. Enter your answers as a comma-separated list.
4. Enter three unspaced capital letters for each permutation.
**Steps to Solve**:
1. **Identify the number of items and the group size**:
- Total items: 6 (A, B, C, D, E, F)
- Number of items to select: 3
2. **Calculate the permutations**:
- The formula for permutations of selecting \( r \) items from \( n \) items is:
\[
P(n, r) = \frac{n!}{(n-r)!}
\]
- For this problem, \( n = 6 \) and \( r = 3 \):
\[
P(6, 3) = \frac{6!}{(6-3)!} = \frac{6 \times 5 \times 4 \times 3!}{3!} = 6 \times 5 \times 4 = 120
\]
- Thus, there are 120 permutations of choosing 3 items from a group of 6.
3. **List permutations of B, D, and F**:
- For three specific items (B, D, F), generate the permutations:
\[
\text{BDF, BFD, DBF, DFB, FBD, FDB}
\]
These permutations are important in helping understand how arrangements are made in different scenarios, whether in mathematics, computer science, or organizing physical and digital objects.
**Optional Show My Work Section**:
- Use this section to detail the steps and reasoning you used to find the permutations.
- This can help in gaining a better understanding, and may also earn bonus points.
**Need Help?**:
- Click the "Read it" button if you need further assistance or examples on how to solve
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman