Assume that there are six final exam to be scheduled at a university. Suppose that the courses are numbered from 1 to 6. Supoose that the following pairs of courses have common students: 1 and 2, 1 and 5, 2 and 3, 3 and 4, 3 and 6, 4 and 5, 4 and 6, 5 and 6. The planning Office wants to Schedule exams so that no student has two exams at the same time. What is the smallest number of time slots that are necessary to achieve this?

Q: Assume that the committee consists of 10 Republicans and 5 Democrats. A subcommittee consisting of 5…

A: Given Information: Assume that the committee consists of 10 Republicans and 5 Democrats. A…

Q: Consider 2 classes, the first with 5 students, and the second with 7 students. From this group of…

A: Given data 2 classes First with 5 students and second with 7 students 2 students need to be selected

Q: ass-code is either a sequence containing a digit followed by 3 letters or a sequence containing 2…

A: The fundamental counting principle says that if n ways are there to complete one thing, and m ways…

Q: Suppose you are at a party with 19 of your closest friends (so including you, there are 20 people…

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Q: Assume that there are 9 girls and 8 boys in the neighborhood club, and a team of 5 is to be…

A: As there are 9 girls and 8 boys now if a team of 5 is to be selected.1) Number of different teams…

Q: Assume that there are 3 pairs of black socks (çorap), 1 pair of pink socks, and 2 pairs of blue…

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Q: In a group of 100 people, each people needs to choose a number from 100 to 120. i)Prove that at…

A: Using the Pigeonhole principle we can prove the first statement. This principle states that if kn+1…

Q: Suppose we have 15 graphics cards and 4 servers. The graphics cards are all identical, but…

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Q: In a group of 100 people, each people needs to choose a number from 100 to 120. i)Prove that at…

A: Given: a group of 100 people, each people needs to choose a number from 100 to 120.

Q: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

A: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

Q: Show that if 5000 boys registered for driving license during the last month(31 days) at driving…

A: Given that 5000 boys registered for driving license during the last month in 31 days at driving…

Q: Be able to demonstrate the fact that at least 10 of the 64 days selected must occur on the same…

A: let we have selected 64 daysThen day 1 is any one week day from 7weekdaysLet day 1 is weekday xAfter…

Q: There are six tutors, four juniors and two seniors, who must be assigned to the 6 hours that a math…

A: Part (a): It is given that there are 6 tutors, four juniors and two seniors. The math center is open…

Q: There are 45 different time periods during which each class at a university can be scheduled. If…

A: to solve the given question, we shall use the Pigeonhole principle. Pigeonhole Principle: If k+1 or…

Q: Imagine a lottery where balls numbered from 1 to 49 are placed in an urn and three are sequentially…

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Q: There are 8 Canadian, 7 German, 6 Chinese, 9 French and 9 Russian students in a class. What is the…

A: Given Data: No. of Canadian=8 No. of German=7 No. of Chinese=6 No. of French=9 No. of Russian=9

Q: (a) Fewer than four marriages will occur in December. (b) At least 14 but not more than 18 marriages…

A: Average marriage per month = 5   The probability of fewer than four marriages is given by Excel…

Q: What is the minimum number of students, each of whom comes from one of the 17 regions, who must be…

A: We have students comes from 17 regions.  Now we will distribute no of students to each of 17…

Q: 4. Find the minimum number of students in a class to be sure that three of them are born in the same…

A: We have to apply the pigeon hole principle to solve this problem.

Q: A 6-digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the…

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Q: Suppose there were 500 nurses graduating this year. Assume that 400 were registered nurses (RN), and…

A: Let RN be the registered nurses, and H be the nurses who plan to work in hospital. From the…

Q: A sonnet is a 14-line poem in which certain rhymingpatterns are followed. The writer Raymond…

A: a). How many sonnets can be created from the 10 in the book? There are 10 possibilities for each 14…

Q: C) There are 20 small towns in a district. A group of 3 people have to be chosen from I of these…

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Q: Eleven graduate students have applied for two available teaching assistantships. In how many ways…

A: In this problem order for the selection is not mentioned therefore we can use combination for award…

Q: The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee…

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Q: What is the minimum number of students, each of whom comes from one of 10 provinces who must be…

A: Let number of students that enrolled = n Number of provinces = 10 Number of pigeon holes = 10 Number…

Q: a committe of 4 is to be selected from 6 men and 5 women. 1 particular man and 1 particular woman…

A: From the given information, there are 6 men and 5 women. That is, the total number of persons is…

Q: Suppose that a department contains 10 men and 18 women. How many ways are there to form a committee…

A: The order of the men/women is not important ( since all selected members will get the same…

Q: A deli wants to line up all of their 20 pre-made sandwiches for display. There are 17 sandwiches…

A: We need to show that there will be 5 regular rolls in a row.

Q: Standard license plates for passenger vehicles in California are of the form NMLMXXX where N is any…

A: GivenThe form of Standard License plates = NMLMXXXN = digit except 0X = any digitL = Upper case…

Q: 6. What is the minimum number of students, each of whom comes from one of the 13 states, who must be…

A: Consider there are 13 students those are from each state that enrolled in a university to…

Q: Assume that there are 10 girls and 8 boys in the neighborhood club, and a team of 8 is to be…

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Q: Suppose that as part of your New Year’s “Get Fit” resolution, you decided to do 10 push-ups each…

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Q: Registrants at a large convention are offered 6 sightseeing tours on each of 3 days. In how many…

A: Number of sightseeing tours for one day are 6. Number of days for the tour is 3.

Q: There is a law made that every man that keeps sheep shall for every 10 sheep, sow one acre of ground…

A: Let the number of sheep he shall keep is 'x'. Given that for every 10 sheep, every man has to sow…

Q: An Internet service provider requires its customers to select a password consisting of fourletters…

A: An Internet service provider requires its customers to select a password consisting of fourletters…

Q: suppose that ten service customers need service call and the maintenance worker can only service…

A: Consider the given information. Total Number of service customers = 10 Number of services done each…

Q: A certain committee consists of 7 people. From the committee, a president, a vice president, a…

A: Solution: We need to choose a committe of a president , a vice president, a , a secretary, and a…

Q: Suppose you are asked to arrange 10 books in a shelf. Three of them are Mathematics, 4 are English…

A: Let us assume there are three women A, B and C sitting beside each other. The different ways in…

Q: A grocery pick-up service has 12 appointment openings one morning. If 8 customers have signed up…

A: Given, there are 12 appointment openings  and 8 customers have signed up already number of ways the…

Q: If the NCAA has applications from six universitiesfor hosting its intercollegiate tennis…

A: a.)For the first year,the NCAA can select the host the event in any one of the 6…

Q: Find the number of arrangements of the digits {0,1,2,3,4,5,6,7,8,9} such that the first digit is…

A: We need to find the total number of arrangements of digits 0,1,2,3,4,5,6,7,8,9 such that the first…

Q: Assume that there are 2 pairs of black socks (çorap),3 pair of pink socks, and 5 pairs of blue socks…

A:

Q: suppose that five service customers need service call and the maintenance worker can only service…

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Q: Suppose that four microchips in a production run of fifty are defective. A sample of six is to be…

A: Suppose that four microchips in a production run of fifty are defective. A sample of six is to be…

Q: Let [A1, A2], [B1, B2], [C1, C2] be 3 married couples who attended a concert.  Show that the number…

A: Consider that G is the group of females and B is the group of males.This two group of G and B can be…

Q: 24 students are about to take an exam. Each student has to pick between wednesday, thursday or…

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Q: What is the minimum number of students, each of whom comes from one of the 50 states, who must be…

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Q: There are 9 periods in each working day of a school. In how many ways can one organize 5 subjects…

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Q: 8. Find the minimum number of students needed to guarantee that 4 of them: (a) have last names which…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.