Homework Help is Here – Start Your Trial Now!
Engineering
Computer Engineering
Кeys We have a box with 21 keys. There are 7 types of keys. Each key is colored (monochromatic) in one of 3 colors: red, green, or blue. Thus, the box contains exactly one key of each combination of type and color. We pick a subset of keys from the box. For cach of the following seven questions, count the number of ways that we can pick a subset satisfying the listed constraints. Your answers must be given in terms of binomials and exponentials. Do not give your answers in terms of factorials. Do not simplify your answers into a single integer. You must use binomials and cxponentials. Use the notation (E) for binomials. At the very beginning of your answer, list your seven expressions in a table as show above. After the table, justify cach of your seven answers, and show your calculations. Formal proofs are not required. 1. Pick 4 red keys. 2. Pick 3 keys, 2 red and 1 blue. 3. Pick 3 keys, 2 red and 1 blue, and no two picked keys are of the same type. 4. Pick 7 keys, one of cach type. 5. Pick 3 keys, all of the same color. 6. Pick 3 keys, no two of the same type. 7. Pick 3 keys, one of cach color, and no two picked keys are of the same type.

Кeys We have a box with 21 keys. There are 7 types of keys. Each key is colored (monochromatic) in one of 3 colors: red, green, or blue. Thus, the box contains exactly one key of each combination of type and color. We pick a subset of keys from the box. For cach of the following seven questions, count the number of ways that we can pick a subset satisfying the listed constraints. Your answers must be given in terms of binomials and exponentials. Do not give your answers in terms of factorials. Do not simplify your answers into a single integer. You must use binomials and cxponentials. Use the notation (E) for binomials. At the very beginning of your answer, list your seven expressions in a table as show above. After the table, justify cach of your seven answers, and show your calculations. Formal proofs are not required. 1. Pick 4 red keys. 2. Pick 3 keys, 2 red and 1 blue. 3. Pick 3 keys, 2 red and 1 blue, and no two picked keys are of the same type. 4. Pick 7 keys, one of cach type. 5. Pick 3 keys, all of the same color. 6. Pick 3 keys, no two of the same type. 7. Pick 3 keys, one of cach color, and no two picked keys are of the same type.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
See similar textbooks
icon
Related questions
Question

please only solve the last part

Кeys We have a box with 21 keys. There are 7 types of keys. Each key is colored (monochromatic) in one of 3 colors: red, green, or blue. Thus, the box contains exactly one key of each combination of type and color. We pick a subset of keys from the box. For cach of the following seven questions, count the number of ways that we can pick a subset satisfying the listed constraints. Your answers must be given in terms of binomials and exponentials. Do not give your answers in terms of factorials. Do not simplify your answers into a single integer. You must use binomials and cxponentials. Use the notation (E) for binomials. At the very beginning of your answer, list your seven expressions in a table as show above. After the table, justify cach of your seven answers, and show your calculations. Formal proofs are not required. 1. Pick 4 red keys. 2. Pick 3 keys, 2 red and 1 blue. 3. Pick 3 keys, 2 red and 1 blue, and no two picked keys are of the same type. 4. Pick 7 keys, one of cach type. 5. Pick 3 keys, all of the same color. 6. Pick 3 keys, no two of the same type. 7. Pick 3 keys, one of cach color, and no two picked keys are of the same type.
Transcribed Image Text:Кeys We have a box with 21 keys. There are 7 types of keys. Each key is colored (monochromatic) in one of 3 colors: red, green, or blue. Thus, the box contains exactly one key of each combination of type and color. We pick a subset of keys from the box. For cach of the following seven questions, count the number of ways that we can pick a subset satisfying the listed constraints. Your answers must be given in terms of binomials and exponentials. Do not give your answers in terms of factorials. Do not simplify your answers into a single integer. You must use binomials and cxponentials. Use the notation (E) for binomials. At the very beginning of your answer, list your seven expressions in a table as show above. After the table, justify cach of your seven answers, and show your calculations. Formal proofs are not required. 1. Pick 4 red keys. 2. Pick 3 keys, 2 red and 1 blue. 3. Pick 3 keys, 2 red and 1 blue, and no two picked keys are of the same type. 4. Pick 7 keys, one of cach type. 5. Pick 3 keys, all of the same color. 6. Pick 3 keys, no two of the same type. 7. Pick 3 keys, one of cach color, and no two picked keys are of the same type.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY
SEE MORE TEXTBOOKS