The grades of students in a Finite Mathematics course at a certain university are determined by their performance on homework, quizzes, three 1-hour exams and a final exam according to the criteria in the following tables.

Q: Suppose that there are nine students in a discrete mathematics class at a small college a) show that…

A: Given: 9 students in a discrete mathematics

Q: Construct NFA for 0*1*0*0 with three states.

A: Answer:

Q: A circuit board has 10 free slots for chips, and four different chips will be installed in it. State…

A:

Q: At a certain company, passwords must be from 4-6 symbols long and composed from the 26 uppercase…

A: Let us consider there n number of objects, and r to be chosen such that repetition is allowed; then,…

Q: A box contains 15 balls in which seven are green and eight are yellow. If five balls must be drawn…

A:

Q: A phone number is a 7-digit that does not start with 0. Call a phone numbers that make up of exactly…

A: According to the permutation rule, if r distinct items are to be chosen from n items without…

Q: Suppose that every student in a discrete mathematics class of 31 students is a freshman, a…

A: Given that, every student in a discrete mathematics class of 31 students is a freshman, a sophomore,…

Q: 1. A coach is trying to see if a new had been using. Design a contro program.

A: In a controlled experiment all the variables in the study remain to be constant except one variable…

Q: Suppose that we have a shipment of 50 microprocessors of which four are defective. In how many ways…

A: Given: shipment of 50 microprocessors of which four are defectiveTo find that:  In how many ways can…

Q: A(n) _______ is an ordered arrangement ofr objects chosen from n objects.

A: We fill the blank space as

Q: A computer programming team has 9 members. (a) How many ways can a group of five be chosen to work…

A: total 9 member

Q: A. Compute the total number of sets (of size 5) containing exactly 2 elements from X and 3 elements…

A:

Q: ) Ifa group of 9 kids have won a total of 100 trophies, then at least one of the 9 kids has won at…

A:

Q: Determine the number of permutations of the set {1 ,2 ,..., 14} in which exactly 7 integers are in…

A: Solution-:

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: 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: Show that A5 has 24 elements of order 5, 20 elements of order 3, and15 elements of order 2.

A:

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: Suppose that in a particular Finite course, 5/14 of students plan on majoring in math, 11/42 plan on…

A: Given information- We have given the proportion of particular Finite course. P (Major in math) =…

Q: Show that A5 has 24 elements of order 5, 20 elements of order 3, and 15 elements of order 2.

A: We know that A5 has only even order permutation. A5 has 5!2=60 elements. Now write the partition of…

Q: A(n) _____ is a collection of items called elements

A:

Q: Show that for all n:  ceil(n) = -floor(-n)

A: In the given question we have to prove that ceil(n)=-floor(-n) That is…

Q: A computer programming team has 9 members. (a) How many ways can a group of five be chosen to work…

A:

Q: Show that if seven integers are selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, there must be…

A:

Q: Suppose that a survery of 100 advertisers in U.S. News, These Times and World found the following.…

A:

Q: How many strings of seven lower case letters of the English alphabet contain exactly four letters w…

A: We have to use permutations and combinations here.

Q: A phone number is a 7-digit that does not start with 0. Call a phone numbers that make up of exactly…

A: A phone number consists of 7 -digit that does not start with 0. To find the possible phone numbers…

Q: What is the minimal number of people needed in a class to ensure that there are two students with…

A: Given information: To ensure that there are two students with the same birthday (the same month and…

Q: Let [A1, A2. [B1, B2, C1, C2 be 3 married couples who attended a concert in Windhoek. a) In how many…

A:

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: b) Use generating functions to determine how many four element subsets of S = {1,2,3, ..,15}…

A:

Q: What is the minimum number of cards that must be drawn from an ordinary deck of cards (52) to…

A: Given problem Given that   The minimum number of cards that must be drawn from a ordinary deck of…

Q: Consider lists made from L, a, T, e, X, with repetitions allowed. How many 4-lists are there in…

A: Please refer to the image below.

Q: Assume that you have 8 dimes and 4 quarters (all distinct), and you select 3 coins. In how many…

A: The number of dimes is 8 and the quarters is 4.

Q: A computer programming team has 9 members. (a) How many ways can a group of five be chosen to work…

A:

Q: How many strings of 7 decimal digits are there, such that at least one of the digit is odd?

A: There are total 10 decimal digits, among which 5 are odd. Since repetition of digits is allowed,…

Q: A computer programming team has 9 members. (a) How many ways can a group of five be chosen to work…

A:

Q: Suppose that there are 27 students in discrete mathematics class. Show that the class must have at…

A: Here we solve this question by contradiction.

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: Founders of a new unnamed company have narrowed the list of names under consideration to 30.…

A: Total number of the names for consideration = 30. The company is considering up to 3 names i.e. the…

Q: 2. Show that the combination of choosing r items from a set of n items has the same possible…

A: Combination can be defined as the number of ways of merging things disregarding of their orders.  It…

Q: A certain committee consists of 20 people. From the committee, a president, a vice-president, a…

A: Given : A certain committee consists of 20 people Now we have to choose a president, a…

Q: andomly selected from a

A: we have given a sample of 6 measurements was randomly selected from normally distributed population…

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

A:

Q: What is the minimum number of students required in a discrete structures class to be sure that at…

A: As we have five grades: k=5 And the number of students: r=9 And we have to calculate: Nk=r N5=9

Q: Suppose that in a particular Finite course, 4/7 of students plan on majoring in math, 25/42 plan on…

A: Given that, in a particular finite course, 47 of students plans majoring in math, 2542 plans…

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: Suppose that in a particular Finite course, 4/7 of student plan on majoring in math, 25/42 plan on…

A: Given Information- 4/7 of student plan on majoring in Math, 25/42 plan on majoring in…

Q: Television and radio stations use four call letters starting with W or​ K, such as WXYZ or KRLD.…

A: the total number of alphabets between A to P is 16.

Q: How many strings of 1our decimal digits have all four digits that are different?

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.