Mr. Jones has 10 books that he is going to put on his bookshelf. Of these, 4 are mathematics books, 3 are chemistry books, 2 are history books, and 1 is a language book. Jones wants to arrange his books so that all the books dealing with the same subject are together on the shelf. How many different arrangements are possible

Q: A math teacher wishes to split a class of thirty students into groups. All groups will work on the…

A: Given data: Total students  = 30 To find: In how many ways can the teacher assign students to the…

Q: The probability that the oldest is a boy and the youngest is a girl, given that there is at least…

A: Here  Family has 3 children with at least one boy and one girl.

Q: You have 6 math books and 6 history books to put on a shelf with five slots. In how many ways can…

A: If a particular event can be done in n different ways and an other event can be done in m different…

Q: There are two roads between towns A and B. There are three roads between towns B and C. How many…

A: There are two roads between towns A and B, and three roads between towns B and C. The number of…

Q: Tom has 16 blue pencils, of which 12 are striped dark blue and light blue, and the rest are solid…

A: There are 16 blue pencils and 9 red pencils out of which 12 are striped dark blue and light blue and…

Q: A professor gives his students 4 essay questions to prepare for an exam. Only 2 of the questions…

A:

Q: Find the number of ways to divide 20 people into Group A (8 people), Group B (7 people) and Group C…

A:

Q: Bryan had some apples. He put 1/3 of the apples and another 4 into basket A, 1/3 of the remaining…

A: Let Bryan had x apples. He put 1/3 of the apples and another 4 into basket A, i.e. x3+4 apples in…

Q: A birthday cake is to have two layers of cake separated by a layer of icing, with another layer of…

A: Given information: The number of layers is 2. The number of kinds of cake is 5. The number of types…

Q: Sarah has to put an outfit on a mannequin every day at her job. if there are 5 shirts, 4 pants,  and…

A: Number of shirts= 5 Number of pants= 4 Number of hats= 8

Q: Jennifer has 4 black bags. She has 15 seeds in the black bags. She has arranged the seeds in the 4…

A: Given : Number of bags = 4 Number of seeds = 15 None of bag is empty and all bags have different…

Q: Paul has 5 books to place on a shelf. How many possible arrangements of all 5 books are there?

A: given data 5 books to place on a shelf. no. of possible arrangements of all 5 books = ?

Q: A donut store has 10 different types of donuts. You can only buy a bag of 3 of them, where each…

A: A donut store has 10 different types of donuts. You can only buy a bag of 3 of them, where each…

Q: The newest cars have 12 different accessories and the buyer pays for each one separately.  If a…

A: Given, The newest cars have 12 different accessories A buyer wants to buy four accessories

Q: There are three light bulbs in a room, and three light switches outside the room. You are outside,…

A: Suppose the three bulbs are B1 , B2 & B3   and                the three switches are S1 , S2…

Q: 9 books in a row on his bookshelf. He will put one of the books, Hamlet, in the first spot. He will…

A: Given Data: Total books: n=9 First spot: One book, Hamlet Last spot:  One book Macbeth   In the…

Q: Mr. Smith decides to organize a potluck party with neighbors on a weekend. John Smith and his wife…

A: Every salad and every dessert should be considered as a different dish here.

Q: Mr Regpala needs the help of 6 students from the class to help him move some supplies. If the class…

A: Given that  Mr Regpala needs the help of 6 students from the class to help him move some supplies…

Q: There are 6 boys and 18 girls in a class. A group of 5 students is needed to work on a project. If…

A:

Q: Your car seats 5 people, including the driver. You have 8 friends who all need you to drive them…

A: Given :  A Car seats 5 people, including the driver. You have 8 friends who all need you to drive…

Q: Alonzo is doing research for the city newspaper on the six topics listed below. He can choose to…

A: According to the given information, it is required to determine the number of ways in which Alonzo…

Q: Each day, Mr. Ling has a boy and a girl summarize the assignment for the day. There are 7 boys and 8…

A:

Q: If there were to be 22 boys and 8 girls at a party and the host wanted each to be given exactly the…

A:

Q: There are two roads between town A and B.There are three roads between town B and C. How many…

A: Number of ways we can travel from A to B is n1 = 2 ways     Number of ways we can travel from B to C…

Q: Dr. Volz gave an exam with 14 questions, but students only had to answer 10 of them. Suppose the…

A: We have to use combination formula. Formula : Crn = n!r!(n-r)!

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.