4 Mathematics books, 3 Chemistry books, 2 Physics books, and 1 Biology book are to be arranged on a bookshelf. How many different arrangements are possible if i. the books in each particular subject must all stand together,  ii. only the Chemistry books must stand together?

Q: In a certain class there are a total of 45 majors in mathematics, 15 majors in philosophy, and 5…

A: Topic = Set theory

Q: A student has five mathematics books four history books, and eight fiction books. In how many diff…

A: Given that A student has five mathematics books four history books, and eight fiction books

Q: How many ways are there to stack an ice-cream come with 4 scoops if the choices are pistachio,…

A: The choices are pistachio, peach, cherry, walnut, peanut butter, and raspberry. That is 6. I scoop…

Q: How many ways can all the dogs be lined up for a photograph, if all the dogs of a similar breed must…

A: Hi thank you for the question. As you have requested solution for the last 2 subparts, we'll answer…

Q: In how many ways can two admirals, three generals, and four lieutenants can be seated in a row of…

A: Given that In how many ways can two admirals, three generals, and four lieutenants can be seated in…

Q: A one-topping pizza consists of choosing a crust, a type of cheese, and one topping. If there are 4…

A:

Q: You have 3 science books, 2 language books, and 4 philosophy books. In how many ways can they be…

A:

Q: A club with ten members is to choose three​ officers: ​ president, vice-president, and​…

A:

Q: (a) How many ways are there to place 10 paintings into 8 boxes, given there should be at least one…

A: a. The total number of ways of dividing 10 paintings into 8 boxes so at least one painting in each…

Q: A class consists of 60 girls and 40 boys. In how many ways can a president, vice-president,…

A: Number of boys=40 Number of girls=60 Given the treasurer must be a girl. Hence the number of ways to…

Q: A group of Mathematics faculty at the local college consists of 10 women and 10 men. Five people are…

A: Given  No of men = 10 No of women = 10 We need to select 5 people

Q: At a corporate dinner, five people including the president and vice president are sitting around a…

A: a) If 5 people sit on a circular table then the number of permutations will be 4!=24 b) If President…

Q: Telephone poles are being stored in a pile with 25 poles in the first layer, 24 in the second 23 in…

A: Given that Telephone poles are being stored in a pile with 25 poles in the first layer, 24 in the…

Q: An equestrian club has ten members. If the club wants to select a president, vice president, and…

A:

Q: For the new fall season, a network president has 11 shows in development, and 8 openings in the…

A: The network president has 11 shows in development . There are eight openings in the prime time…

Q: A certain congressional committee consists of 8 senators and 12 representatives. How many ways can a…

A: It is given the number of senators is 8 and representatives is 12.

Q: There are 4 different Mathematics books and 5 different Science books. In how many ways can the…

A: 4 different Mathematics books  And,                              5…

Q: 5. How many arrangements can be made from 4 boys and 4 girls if they have to sit in a roundtable and…

A: We have given that  Number of boys=4 Number of girls=4

Q: Six math books, four physics books and three chemistry books are arranged on a shelf. How many…

A:

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: There are 7 Math books, 4 English books and 6 Filipino books on a shelf. How many ways can you…

A: Permutation: Permutation means finding a number of ways to arrange a specified number of distinct…

Q: A club with 5 members is to choose 3​ officers: ​ president, vice-president, and​…

A:

Q: In a certain class there are a total of 29 majors in mathematics, 21 majors in philosophy, and 7…

A:

Q: A committee of 6 people, with three of the six to be designated chair, vice-chair, and secretary, is…

A: 5. In a group there are 15 people. A committee of 6 people has to be selected, in which 3 must be…

Q: A club with 17 members must choose a president, a vice president, a treasurer, and a secretary. How…

A:

Q: A student has 4 different biology books, 4 different chemistry books, and 5 different physics books.…

A:

Q: The board of directors of a corporation must select a president, a secretary, and a treasurer. In…

A: Given that there are total 14 members.    A president, a secretary, and a treasurer represent 3…

Q: The board of directors of a corporation must select a president, a secretary, and a treasurer. In…

A:

Q: There are 10 people to be selected from. How many committees are possible?

A: Here use combination

Q: Delegates from 10 countries, including Russia, France, England, and the United States, are to be…

A: Given  10 countries in total  4 of them are Russia, France, England, United States  We need to…

Q: A food committee prepared 3 kinds of sandwiches, 5 drinks, 4 fruits and three candies. How many…

A: Given: A food committee prepared 3 kinds of sandwiches, 5 drinks, 4 fruits and three candies.   To…

Q: A club with eleven members is to choose three​ officers: ​ president, vice-president, and​…

A: A club with eleven members is to choose three​ officers: ​ president, vice-president, and​…

Q: (a) If first prize is $100, second prize is $80, and third prize is $30, in how many different ways…

A: Given: People buy raffle tickets = 200

Q: A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated…

A:

Q: 1. A college freshman must take a science course, a humanities course, and a mathematics course. If…

A:

Q: How many ten-digit telephone numbers are possible if the first three digits must all be different?

A: Given,total no.of digits=10  (0 to 9)

Q: A man has 4 shirts, 4 pairs of trousers, 3 pairs of socks and 2 pairs of shoes. How many different…

A: Given Number of shirts = 4 Number of trousers = 4 Number of pair of socks = 3 Number of pair of…

Q: Your professor has 10 advanced statistics texts and 8 advanced calculus texts. (a) How many ways can…

A:

Q: There are 4 different Mathematics books and 5 different Science books. In how many ways can the…

A:

Q: The board directors of a corporation must select a president, a secretary, and a treasurer. In how…

A: We will use arithmetic method to find solution to the problem.

Q: I have nine books and have room to display only four of them at a time on my bookself. how many…

A:

Q: In a certain class there are a total of 37 majors in mathematics, 18 majors in philosophy, and 5…

A:

Q: In how many ways can 4 AIRFORCE and 5 ARMIES be seated on a bench if the ARMIES must  be seated…

A:

Q: 2. A plate number is made up two consonants followed by How many plate numbers are possible. a. if…

A: A plate number is made by two consonants, three non-zero digits and vowel.

Q: A Maryland automobile license plate consists of three letters followed by three numbers.  How many…

A: As per bartleby guidelines only one question should be answered once, please upload each question…

Q: The board of directors of a corporation must select a president, a secretary, and a treasurer. In…

A:

Q: Suppose a department contains 12 men and 15 women. How many ways are there to form a committee with…

A: According to the question  number of combination are

Q: 2) Phone numbers consist of a three-digit area code followed by seven digits. If the area code must…

A: Given information- We have given that a phone number consist of a three-digit area code followed by…

Q: A certain student organization has 17 members - 7 math majors and 10 english majors. A committee of…

A: Total number of students = 17;  7 math majors and 10 English majors.

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.