There are 9 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?

Q: Find the number of ways to put eight different books in five boxes, if no box is allowed to be…

A:

Q: How many combinations can the seven colors of the rainbow be arranged into groups of three colors…

A:

Q: From 9 different books of which 3 books are about mathematics, how many groups of 5 books each can…

A: The formula for combination is nCr= n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)] / r!.…

Q: Twelve teachers are to be assigned to three schools. In how many ways can this be done if: a…

A: Given Twelve teachers are to be assigned to three schools

Q: There are 2 copies each of 4 different books. In how many ways can they be arranged on a shelf?

A:

Q: A club with 29 members is to select a committee of five persons. In how many ways can this be done?

A: In a committee, we select the persons as a group. So the arrangement does not matter. So we will use…

Q: Suppose a class consists of 4 students majoring in Mathematics, 3 students majoring in Islamic…

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Q: How many ways can we assign 124 students to 4 sections in such a way that Section 1 must have at…

A: Given: There are 124 students and 4 sections Section 1 must have at least 30 students, section 2…

Q: Assume that you have a committee of 11 members, made up of 6 men and 5 women. In how many ways can…

A: Determine the number of ways can the 3 tasks be assigned so that both men and women are given…

Q: Assume that you have a committee of 15 members, made up of 9 men and 6 women. In how many ways can…

A:

Q: How many ways can 120 unique packages be loaded into 10 delivery trucks where each truck must have…

A: 120 distinct packages have to be distributed equally among the 10 trucks.

Q: With 20 people seated around a tabke, how many ways can 3 people be selected without any being…

A: It is given that there are 20 people seated around a table. The total number of ways of selecting 3…

Q: Five of ten books are arranged on a shelf. In how Many waYS Can this be done?

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Q: A credit card company gives each of its customers a 4-digit PIN where each digit is selected from…

A: Multiplication rule of counting:If a task consists of a sequence of choices in which there are ‘a’…

Q: there are 11 members on a board of directors. if they must form a subcommittee of 6 members, how…

A: we use the probability for selections formula, nCr = n!/(n-r)! * r!

Q: A combination lock uses 4 numbers, each of which can be 0 to 29. If there are no restríctions on the…

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Q: How many outfits can be constructed with 1 shirt, 1 pants, and 1 tie from a wardrobe of 2 shirts, 5…

A: The given problem is based on combination {Because order doesn't matter}. The combination of…

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: There are 10 students in a class. In how many ways can an instructor give at least one student a…

A: There are 10 students So sample size, n= 10 And we've to find ways for at least 1 student. So r= 1

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

A: Consider the number of members is 18. The number of posts is 3. Then, the total number of ways in…

Q: A state makes license plates with two letters followed by four numbers. if no repetitions of the…

A: The license plates must consist of two letters followed by four numbers.

Q: If there are 1022 different classes at a university, how many different rooms are required in order…

A: according to question, 1022 different classes are there at a university and we have to schedule all…

Q: Assume that a grade of A,B,C,D, or F is assigned to each of 9 students. In how many ways can grades…

A: From the provided information, The grades are A, B, C, D or F Total students = 9

Q: There are 10 people in a meeting. In how many ways can you arrange your participants around a ROUND…

A: Total ways in which 10 people be arranged around a round table so that 4 people sit beside each…

Q: What is the number of ways to color n objects with 3 colors if every color must be used at least…

A: Given that there are n objects and 3 colors.   The three colors must be used at least once. That is,…

Q: From 6 English teachers and 5 Mathematics teachers, committee of 5 teachers will be organized. How…

A:

Q: A traveling agent has to visit four cities, each of them five times. In how many different ways can…

A: There are 205! 5! 5! 5!ways to visit 4 cities, each of them 5 times.

Q: There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects…

A: * SOLUTION :-  from the given information the calculation is provided as below

Q: Consider a necklace that is made up of 8 different gems stone such that ruby is always between…

A: As per our guidelines we can answer only one question. please repost other seperately.    7.

Q: How many seven-digit numbers can be made from the digits 1 to 9 if repetition is allowed?

A: Given that  To find the number of ways of 7 digit number can be made from the 1 to 9

Q: In how many way, can a manager arrange 16 employees into 8 groups

A: Combination is a collection of the objects where the order does not matter

Q: In a certain state, all car license plates have four capital letters followed by three digits. How…

A: Given Car license plates have 4 (A to Z) capital letters followed by 3 (0 to 9) digits

Q: A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes…

A: Here , particular brand of shirt comes in 12 colors. It has female version and male version. And it…

Q: 10 identical copies of a movie will be stored on 40 computers such that each computer has at most 1…

A: Given the statement. 10 identical copies of a movie will be stored on 40 computers such that each…

Q: In a group of 4 people, is it possible for each person to have exactly 3 friends? Why?

A: Let G be a graph with 4 vertices, one vertex representing each person in the group. Join two…

Q: In how many ways can 3 blue books and 4 red books be arranged on a shelf if a red book must be on…

A: The number of ways in which n different objects can be arranged, is given by n!, where,…

Q: In how many way, can a manager arrange 15 employees into 3 groups

A: Number of ways = 15C3

Q: bookshelf has space for exactly 12 books. In how many ways can the books be arranged on the…

A:

Q: A manufacturing company has 5 employees. Each employee is assigned to one of three shifts: the day…

A: Given, a manufacturing company has 5 employees and each employee is assigned to one of three shifts:…

Q: The manufacturer plans to make scarves with 8 colored stripes. There are 16 colors to choose from…

A:

Q: Assume that a bakery has 7 different types of cakes. How many different ways can 5 cakes of any type…

A: We have total 7 cakes  From the 7 cakes, we have to pick a group of 5 cakes. So the arrangement does…

Q: A total of 50 students are in a class and they are to be divided into groups of 5. How many…

A: Ans - Given,       A total of 50 students are in a class and they are to be divided into groups of…

Q: How many license plates are possible if they consist of 1 digit followed by 1 letter followed by 5…

A:

Q: From a group of 14 newly hired office​ assistants, 5 are selected. Each of these 5 assistants will…

A: Given dataNo of newly hired assistants = 145 to be selected5 assistant can be selected in 14C5…

Q: 2) A class has 25 students. Each day, three students are chosen to present their work at the board.…

A:

Q: How many ways can a local chapter of the American Chemical Society Schedules 3 speakers for 3…

A: As Dr. S. N. De said "A permutation of a set is defined as an arrangement of its members into a…

Q: A five-person committee is to be selected from an organization's membership of 19 people. How many…

A: It is given that, An organization has 19 people out of which 5 person committee is to be selected.…

Q: How many four-digit numbers can be made from the digits 1 to 6 if repetition is allowed?

A: Number of four digit can be made from digits  1 to 6 :

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

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.