Question

1) A computer class has 28 students, all in their 1st, 2nd, or 3rd year. A)...

1) A computer class has 28 students, all in their 1st, 2nd, or 3rd year.

A) Show that there are at least ten students in the class who are in the same year.

B) How many students would have to be added to the class, at least, to ensure that at least 12 are in the same year?

Homework Answers

Answer #1

A.

Even in the worst case, there have to be 9+9+10.

Since this combination also satisfies the condition of at least ten students in one class, any other combination will also satisfy it.

If any student is replaced from one class to the other, the number of students have to be 10 in at least one class.

B.

There are already 28 students. to ensure that there are at least 12 of the same year, we would need 34 students in the class.

Thus, 6 students would have to be added in the class, to ensure that there are at least 12 in the same class.  

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Professor N. Timmy Date has 28 students in his Calculus class and 20 students in his...
Professor N. Timmy Date has 28 students in his Calculus class and 20 students in his Discrete Mathematics class. (a) Assuming that there are no students who take both classes, how many students does Professor Date have? (b) Assuming that there are five students who take both classes, how many students does Professor Date have?
Let Aequals=left bracket Start 2 By 2 Matrix 1st Row 1st Column 1 2nd Column 2...
Let Aequals=left bracket Start 2 By 2 Matrix 1st Row 1st Column 1 2nd Column 2 2nd Row 1st Column 8 2nd Column 18 EndMatrix right bracket 1 2 8 18 ​, Bold b 1b1equals=left bracket Start 2 By 1 Matrix 1st Row 1st Column negative 5 2nd Row 1st Column negative 36 EndMatrix right bracket −5 −36 ​, Bold b 2b2equals=left bracket Start 2 By 1 Matrix 1st Row 1st Column 3 2nd Row 1st Column 16 EndMatrix right...
4.How many students in a class must there be (smallest size) to ensure that at least...
4.How many students in a class must there be (smallest size) to ensure that at least 10 students get the same grade (one of A, B, C, D, F, or N)? (Using the pigeonhole principle) (Please explain it, finding the principle difficult to understand. Thank you!)
At a university all students must take a test to see if they understand campus polices....
At a university all students must take a test to see if they understand campus polices. The test has 6 multiple choice questions, each with three possible answers and only one right answer per question. This year every student got at least two questions right. How many possible ways could the students have answered the test questions? The incoming class this year has 541 students. Prove that at least two students answered the test in the exact same way.
An art class has 10 students in it. All of them must present their portfolios and...
An art class has 10 students in it. All of them must present their portfolios and explain their work to the instructor and their classmates at the end of the term. How many presentation orders are possible if: a) the student names are drawn from a hat to determine who goes first, second, and so on? b) the student names are put in alphabetical order to determine who goes first, second, and so on?
At a university all students must take a test to see if they understand campus polices....
At a university all students must take a test to see if they understand campus polices. The test has 6 multiple choice questions, each with three possible answers and only one right answer per question. This year every student got at least two questions right. How many possible ways could the students have answered the test questions? The incoming class this year has 531 students. Prove that at least two students answered the test in the exact same way. Please...
November 1st, 2020: All 200 students of ABC class at HKU buy Tesla Care warranty protection...
November 1st, 2020: All 200 students of ABC class at HKU buy Tesla Care warranty protection from Tesla Inc. for which they pay $10,000 each for their Tesla cars. They each pay Tesla cash of 10,000 each on November 1st for the contract. The Tesla Care contract lasts 2 months and allows students to replace their Tesla Car battery if the battery fails within the 2 months until December 31st, 2020. Once Tesla provides a replacement battery, the contract expires,...
(1 point) A class survey in a large class for first-year college students asked, "About how...
(1 point) A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 278 students was x⎯⎯⎯ = 147 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation σ = 65 minutes in the population of all first-year students at this university. Use the survey result to give a 90% confidence interval for the mean study...
A class contains 30 students. 1) The teacher asks three questions during a class, which any...
A class contains 30 students. 1) The teacher asks three questions during a class, which any student can answer. How many unique outcomes? 2) The class is divided into 6 teams of 5 students each, numbered team #1 thru #6. Each team is to make a presentation. How many different ways can the team presentations be sequenced? 3) A team of 8 students is to be selected from the class. In how many unique ways can this team be selected?...
[Note: The order of jobs in a schedule is 1st,2nd,3rd,4th,5th, for A,B,C,D,E, respectively.] The jobs A,B,C,D,E,...
[Note: The order of jobs in a schedule is 1st,2nd,3rd,4th,5th, for A,B,C,D,E, respectively.] The jobs A,B,C,D,E, arrived in that order to be processed on two machines. Job A B C D E Time on Machine 1 40 48 58 26 70 Time on Machine 2 37 60 56 48 72 Question 6. Which is the Johnson’s Rule schedule?      (A) ‘DBECA’     (B) ‘ACEBD’     (C) ‘DCABE’     (D) ‘DABEC’   (E) none of the above Question 7. Consider the FIFO schedule of (A,B,C,D,E)....