Refer to a set of five distinct history books, three distinct biology books, and two distinct philosophy books. In how many ways can these books be arranged on a shelfo а. b. In how many ways can these books be arranged on a shelf if all five history books are placed on the lefto

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

A: Given that there are 15 graphics cards and 4 servers. All the graphic cards are identical, but the…

Q: A fleet of nine taxis is to be dispatched to three airports in such a way that two go to airport A,…

A: Given, A fleet of 9 taxis is to dispatch to the three airports A, B, and C also, 2 go to A, 6 go to…

Q: a) Suppose in a university, each subject offered to students has a subject code consisting of four…

A: a) In a university each subject offered to students has a subject code consisting of four letters…

Q: (Assume that in a university with 1000 students. 200 students are taking a course in mathematics,…

A:

Q: Suppose you are taking a bus trip from your home in Florida to California. There are seven different…

A: Given that we are taking a bus trip from your home in Florida to California. There are seven…

Q: Mr. Jones has 10 books that he is going to put on his bookshelf. Of these, 4 are Math books, 3 are…

A: Given:- total books =10 maths books =4 Chemistry books =3 history books =2 song lyric book =1

Q: How many 3-letter codewords can be formed if: At least one of the letters is to be chosen from the…

A:

Q: How many ways are there to choose two subsets A and B of [n] so that A ⊆ B, and |B| is even

A: Using logic of sets and subsets we will solve the problem. Using facts we will find a solution to…

Q: Consider a bag containing five red marbles, two green ones, one transparent one, five yellow ones,…

A:

Q: There are five distinct computer science books, three distinct mathe- matics books, and two distinct…

A:

Q: There are five distinct computer science books, three distinct mathematics books, and two distinct…

A:

Q: Suppose there are 8 roads connecting town A to town B and 4 roads connecting town B to town C. In…

A: Solution: From the given information, there are 8 roads connecting town A to town B and 4 roads…

Q: In how many ways can the car be ordered?

A: Given :  n1 = number of colour = 8  n2 = number of styles = 2

Q: uppose there are 6 freshman, 10 sophomores, 12 juniors, and 14 seniors running for the offices of…

A: Given data, Number of freshman=6 Number of sophomores=10 Number of juniors=12 Number of seniors=14…

Q: 4-person grievance committee is to be selected out of 2 departments, A and B, with 15 and 25 people.…

A:

Q: (b) Every student in a discrete math class is either a computer science or a mathematics major or is…

A: The union of events A and B is defined as n(A ∪ B) = n(A)  + n(B) – n(A ∩ B).

Q: a. if the characters should not repeat? b. if the characters repeat? c. if the first 3 characters…

A: Given: A social media account requires a 6-character password. Passwords should only contain numbers…

Q: A clothing store has a certain shirt in four sizes: small, medium, large, and extra-large. If it has…

A: Given: The number of small-sized shirts is 3. The number of medium-sized shirts is 4. The number of…

Q: If there are nine distinct items 3 at a time, how many permutations will there be

A:

Q: From the digits 1,2,3,4,5,7 and8 a) How many numbers of four different digits each can be formed? b)…

A: Given  The digits 1,2,3,4,5,7and 8  a). How many numbers of four digits each can be formed. b). How…

Q: In how many different ways can the letters of the word wombat be arranged?

A: The number of ways n distinct objects can be arranged is equal to n! . The value of n! is calculated…

Q: how many different ways can the letters of the word wombat be arranged if the letters wo must remain…

A: Using Permutation and Combination we can solve for different ways

Q: In how many ways can 3 novels, 4 mathematics books, and 1 biology book be arranged on a bookshelf if…

A: Given, 3 Novels N1, N2, N3 4 Mathematics M1, M2, M3, M4 1 Biology B1

Q: Consider five-digit numbers  = a1 a2 a3 a4 a5, with each digit from the set {1, 2, 3, 4}. a. How…

A: Solution is given as below:

Q: Consider the numbers 2, 4, 5, 7 and 8. If repetition is not allowed, how many three digit numbers…

A: Solution To make the 3 digit number we will use permutation.

Q: how many different ways can the letters of the word JOYRIDE be arranged such that all letters are…

A:

Q: a. A fleet of sixteen taxis is to be dispatched to three airports in such a way that three go to…

A: here AS PER GUIDELINES I HAVE CALCULATED FIRST MAIN QUESTION , AS YOU POSTED A AND B TOTALLY…

Q: Refer to a set of five distinct history books, three distinct biology books, and two distinct…

A: Factorial Rule: The total number of ways n different objects can be arranged where the order of the…

Q: Assuming the roles of president and secretary cannot be filled by the same person, how many ways are…

A: When Tyler is chosen as president, we have 3 choices for the post of secretary. So there are 3 such…

Q: Five people plan to meet after school, and if they all show up, there will be one group of five…

A: Five people plan to meet after school. We have to find the number of ways if three of them show up.

Q: Suppose that in a certain state, all automobile license plates have three uppercase letters followed…

A: There are 26 letters [A-Z] and 10 digits [0-9] d) If the letters and digits are distinct then we can…

Q: In how many different ways can a panel of five on-off switches be set if no two adjacent switches…

A: Five on-off switches to be set such that no two adjacent switches can be off. Case 1 : First switch…

Q: a. In how many different ways can the letters of the word computer be arranged if the letters co…

A:

Q: 17) How many elements are in the union of four sets if the sets have 100, 150, 250, and 400…

A: Here, n(A)= 100, n(B), 150, n(C)=250, n(D)=400 n(A∩B)=15, n(A∩C)=15, n(A∩D)=15, n(B∩C)=15,…

Q: Assume that the committee consists of 11 members including Cecil. The same three offices are to be…

A: n = 11 members positions = 3 Problem can be solved using the concept of permutation and combination.

Q: Suppose we want to choose 5 objects, without replacement, from 17 distinct objects. (a) If the order…

A: We will the number of ways in both conditions as following.

Q: If all the letters of the word ARRANGE are arranged in all possible ways, in how many of words we…

A: Permutations and combinations are two methods in mathematics. Permutation deals with arrangements…

Q: A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each…

A: Solution: A standard deck of cards  consists  total of 52 cards.  A standard deck of cards consists…

Q: How many five-card hands (drawn from a standard deck) contain exactly two spades? (A five-card hand…

A: There are 13 spades in a deck of 52 cards. We can select 2 spades in 13C2=78 ways.

Q: Suppose that two letters are to be selected from A, B, C, D, and E and arranged in order. How many…

A: Given: Two letters are to be selected from A, B, C, D, and E and arranged in order. There are in…

Q: Suppose there are 14 freshman, 13 sophomores, 15 juniors, and 17 seniors running for the offices of…

A: There are 14 freshman, 13 sophomores, 15 juniors and 17 seniors.

Q: A. How many arrangements of all letters can be made from the word COPROCESSORS

A: The given word is COPROCESSORS"

Q: Three different classes contain 20, 18, and 25 students, respectively, and no student is a member of…

A:

Q: 2) How many elements are in the union of 5 sets if the sets contain 10,000 elements, each pair of…

A: Given that there are 5 sets and sets contains 10,000 elements, each pair of sets has 1000 elements,…

Q: From among the 36 students in a class, one president, one vice-president and secretary are to be…

A: It is given that, there are 36 students in a class. Out of which one is elected for president, one…

Q: In how many ways can you arrange books of the on a shelf if there are 4 of the same kind of Math…

A:

Q: Suppose there are 6 girls and 6 boys in a class. In how many ways can you arrange these children in…

A: Permutations and combinations

Q: (a) How many 4-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, and 7, if each digit…

A: Permutation: A permutation of a set is defined as an arrangement of its members into a sequence or…

Q: A certain brand of shoes comes in 2 different styles, with each style available in 10 distinct…

A: Different style = a = 2 Distinct color = b = 10

Q: A given large basket can contain 70 pieces of fruit consisting of apples, bananas, kiwifruit,…

A: