i) If you have twenty ones and fifteen zeroes how many ways can we arrange these digits such that no two zeroes are adjacent? ii) Show that the number of subsets of a finite set S is 2 |S| iii) [The Birthday Problem] What is the probability that at least one of ten people are born on the same day of the year? [Note: as the number of people increase a surprising result occurs] ** [Hint:
i) If you have twenty ones and fifteen zeroes how many ways can we arrange these digits such that no two zeroes are adjacent? ii) Show that the number of subsets of a finite set S is 2 |S| iii) [The Birthday Problem] What is the probability that at least one of ten people are born on the same day of the year? [Note: as the number of people increase a surprising result occurs] ** [Hint:
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
Solve all
![i) If you have twenty ones and fifteen zeroes how many ways can we arrange these digits such that
no two zeroes are adjacent?
ii) Show that the number of subsets of a finite set S is 2 |S|
i) [The Birthday Problem] What is the probability that at least one of ten people are born on the
same day of the year? [Note: as the number of people increase a surprising result occurs] ** [Hint:
What is the probability ALL have different birthdays?]
iv) You have Eight Boys and Seven Girls. How many ways can you arrange three boys and two girls
for a picture?
** [Hint: consider first the arrangement positions 1, 2,3 are boys and 4 ,5 are girls ** how many
ways cant this be done
Next: How many ways can we CHOOSE three positions out of 1,2,3,4,5 to put boys and the rest to
put girls?]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfdf176a-8014-4f8f-9292-9633da8518c8%2F6be85730-8473-4a3c-9aa4-61abac38d3b0%2F5twxc1_processed.png&w=3840&q=75)
Transcribed Image Text:i) If you have twenty ones and fifteen zeroes how many ways can we arrange these digits such that
no two zeroes are adjacent?
ii) Show that the number of subsets of a finite set S is 2 |S|
i) [The Birthday Problem] What is the probability that at least one of ten people are born on the
same day of the year? [Note: as the number of people increase a surprising result occurs] ** [Hint:
What is the probability ALL have different birthdays?]
iv) You have Eight Boys and Seven Girls. How many ways can you arrange three boys and two girls
for a picture?
** [Hint: consider first the arrangement positions 1, 2,3 are boys and 4 ,5 are girls ** how many
ways cant this be done
Next: How many ways can we CHOOSE three positions out of 1,2,3,4,5 to put boys and the rest to
put girls?]
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 4 steps
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,
