t is the maximum number of people needed to be sure that at most three of them have a birthd th? Why?
t is the maximum number of people needed to be sure that at most three of them have a birthd th? Why?
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
![**Question:**
What is the maximum number of people needed to be sure that at most three of them have a birthday during the same month? Why?
This can be approached using the pigeonhole principle in combinatorics.
Given that there are 12 months in a year, we want to find the maximum number of people such that each month has at most three people with a birthday.
If there are 12 months and each month can have up to three people with a birthday without exceeding this number, then the maximum number of people can be calculated as:
\[ 12 \times 3 = 36 \]
Therefore, the maximum number of people needed to ensure that at most three of them have a birthday in the same month is 36.
If a 37th person were added, they would have to have a birthday in a month that already has 3 people, thereby exceeding the limit. Hence, 36 people is the maximum number to ensure that no more than three of them share the same birth month.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc59b3e01-f4fe-4ed0-a002-b05c91db4102%2Fa58d504b-f33f-43be-a934-aa15b0eb51a0%2Fqd4c00r_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
What is the maximum number of people needed to be sure that at most three of them have a birthday during the same month? Why?
This can be approached using the pigeonhole principle in combinatorics.
Given that there are 12 months in a year, we want to find the maximum number of people such that each month has at most three people with a birthday.
If there are 12 months and each month can have up to three people with a birthday without exceeding this number, then the maximum number of people can be calculated as:
\[ 12 \times 3 = 36 \]
Therefore, the maximum number of people needed to ensure that at most three of them have a birthday in the same month is 36.
If a 37th person were added, they would have to have a birthday in a month that already has 3 people, thereby exceeding the limit. Hence, 36 people is the maximum number to ensure that no more than three of them share the same birth month.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 1 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,
