MATH 140 - Lecture 8 Worksheet 1. (a) How many lists of length 3 are there, if the first two entries are letters from the English alphabet, and the last entry is a number? (b) How many lists of length 4 can be made from the letters A,B,C,D, if repetitions are allowed? (c) How many lists of length 4 can be made from the letters A,B,C,D, if repetitions are not allowed? (d) How many lists of length 3 can be made from the lottora RCD :C
MATH 140 - Lecture 8 Worksheet 1. (a) How many lists of length 3 are there, if the first two entries are letters from the English alphabet, and the last entry is a number? (b) How many lists of length 4 can be made from the letters A,B,C,D, if repetitions are allowed? (c) How many lists of length 4 can be made from the letters A,B,C,D, if repetitions are not allowed? (d) How many lists of length 3 can be made from the lottora RCD :C
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
How can we complete questions 1a-1e?
![**MATH 140 - Lecture 8 Worksheet**
1.
(a) How many lists of length 3 are there, if the first two entries are letters from the English alphabet, and the last entry is a number?
(b) How many lists of length 4 can be made from the letters A, B, C, D, if repetitions are allowed?
(c) How many lists of length 4 can be made from the letters A, B, C, D, if repetitions are not allowed?
(d) How many lists of length 3 can be made from the letters A, B, C, D, if repetitions are not allowed and each list must contain "C"?
(e) A byte is an 8-digit binary string, which is a list of 1’s and 0’s. How many such byte strings are there? How many end in 0? How many have the second and fourth digit as 1’s?
2.
(a) Compute 3!, 4!, 5!, 10!.
(b) How many 9-digit numbers (using 1, 2, 3, ..., 9) are there if repetition is not allowed? How many are there which have at least one digit repeated?
(c) Compute \(\frac{100!}{98!}\).
The calculation shown is:
\[
= \frac{100 \cdot 99 \cdot 98!}{98!} = 100 \cdot 99 = 9900
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38e21668-df36-4535-9b97-aa4a56ba16f0%2Fd2f19ab2-6294-4041-8f18-abd953bd5e36%2Fsdgieg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**MATH 140 - Lecture 8 Worksheet**
1.
(a) How many lists of length 3 are there, if the first two entries are letters from the English alphabet, and the last entry is a number?
(b) How many lists of length 4 can be made from the letters A, B, C, D, if repetitions are allowed?
(c) How many lists of length 4 can be made from the letters A, B, C, D, if repetitions are not allowed?
(d) How many lists of length 3 can be made from the letters A, B, C, D, if repetitions are not allowed and each list must contain "C"?
(e) A byte is an 8-digit binary string, which is a list of 1’s and 0’s. How many such byte strings are there? How many end in 0? How many have the second and fourth digit as 1’s?
2.
(a) Compute 3!, 4!, 5!, 10!.
(b) How many 9-digit numbers (using 1, 2, 3, ..., 9) are there if repetition is not allowed? How many are there which have at least one digit repeated?
(c) Compute \(\frac{100!}{98!}\).
The calculation shown is:
\[
= \frac{100 \cdot 99 \cdot 98!}{98!} = 100 \cdot 99 = 9900
\]
Expert Solution
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 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
