If four students out of 35 students in a classroom are chosen to have lunch with the principal how many ways can the students be chosen

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: There are 23 students in a class, and 6 of them will be chosen to go on a field trip. How many ways…

A:

Q: Suppose you are to arrange 9 people on a line. If 5 specific people require to be following each…

A: Given,total no.of people=9

Q: A group of 5 students is to be chosen from a 30 student classroom. How many ways can this be done?

A: Note that here we have to select a group of 5 students from a 30 student classroom.

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

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Q: There are 4 buses running between two cities. In how many ways can a man go from one city to other…

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Q: How many ways can we pair up 24 dogs with 24 cats for example one dog to one cat?

A: We have to pair 24 dogs with 24 cats

Q: A class of 50 students consists of twenty four boys and 26.how many different ways can 5 students be…

A: Given: A class of 50 students with 24 boys and 26 girls are there. Now ,total of 5 students are…

Q: There are 13 students in a class , and 6 of them will be chosen to go on the field trip . How many…

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Q: How many ways are there to fly from City 1 to City 4 with one stop?

A: Here use given table for no of ways fly from city 1 to city 4

Q: Five friends have tickets next to each other in one row. If two of the friends must sit next to each…

A: Five friends have tickets next to each other in one row. Two of the friends must sit next to each…

Q: Suppose that a department contains 10 men and 15 women. How many ways are there to form a committee…

A:

Q: How many ways that two girls and 4 boys can fall in a line of there must be a girl and a boy in the…

A: Let us assume there are three persons A, B and C sitting beside each other. The different ways in…

Q: If there are 13 possible project topics and 6 students must choose from the available topics, how…

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

A: GivenTwo copies each of 4 different booksTotal no.of books=2×4=8

Q: If there are 3 representatives from Company A and 4 representatives from Company B meet. If they…

A: This is a application of Fundamental Principle of Counting .

Q: There are 6 women and 9 men signed up to join a swing dance class. In how many ways can the…

A: Given Information: There are 6 women and 9 men signed up to join a swing dance class. We are asked…

Q: A camp counselor and four campers are to be seated along a picnic bench. And how many ways can this…

A: given, A camp counselor and four campers are to be seated along a picnic bench. No of ways of…

Q: There are 13 female board members and 17 male board members. How many ways are there to make a…

A: Given there are 13 female board members and 17 male board members. To find number of ways are there…

Q: A time traveler can take 5 books with him, and he has 76 books to choose from. How many different…

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Q: Cikgu Yati asked five of her pupils how many of the five of them had studied the day before. Jimmy…

A: Consider Jimmy for once, if he would have been telling the truth then no one including Jimmy would…

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

A:

Q: There are 9 women and 8 men signed up to join a swing dance class. In how many ways can the…

A: Given:  no of women=9  no of men=8  nonof ways to choose 8 people to join 2 or fewer must be men??

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: Suppose you have 11 books and you randomly pick 4 to take on vacation with you. How many ways can…

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Q: A small town have five police cars: when a call comes in the dispatcher may dispatch no cars, one…

A: Given that there are 5 cars.  The dispatcher may dispatch no cars, one car, two cars, three cars,…

Q: The price of a European tour includes four stopovers to be selected from among 10 cities. In how…

A: Given data, No of cities(n)=10 No of stopovers(r)=4

Q: Suppose, you have 3 different caps, 4 different shirts, 3 different pants and 3 pairs of socks and 2…

A: Depends on given data total outfits 3x4x3x3x2= 216  No need to wear socks and caps So total ways…

Q: You have 10 concert tickets to distribute among 15 friends.  Of the 10 tickets, six have assigned…

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Q: If 10 people come from different places and shake hands in how many different way could this be done

A: The formula for the number of handshakes possible with n people is          handshakes = n*(n -…

Q: There are 10 doors to a coliseum. In how many ways can a person go in and out if one can enter any…

A: There are 10 doors to a coliseum . A person can go in in 10 ways.

Q: There are 24 books on a shelf. How many ways are there to choose 10 of them so that no two of the…

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Q: A student must take 4 courses. In how many ways can they do that if there are 8 courses and 1 is…

A: Solution

Q: Suppose there are 20 students in our class and we want to choose 3 to sit in the front row. How many…

A: Given information There are 20 students We want to choose 3 to sit in the front row Total number of…

Q: 2. If a license plate consist of 3 letters followed by 3 digits, how many license plates are…

A: Here the repetition of letters and numbers are allowed.

Q: There are 15 persons in a party and if each 2 of them shakes hands with each other, how many ways…

A: Given data: 15 persons in a party Each 2 of them shakes hands with each other

Q: If there are 5 ways to perform task A and 6 ways to perform task​ B, then how many ways are there…

A: Given information No of ways to do task A = 5 No of ways to do task B = 6

Q: A committee of 6 U.S. senators is to be formed with 3 Democrats and 3 Republicans. In how many ways…

A: Combination Rule:A combination is a selection of all or part of a set of objects, without regard to…

Q: Suppose that we have 10 numbered blocks, 2 RED, 3 BLUE, 4 GREEN, and one WHITE.  How many ways can…

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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: Your club would like to form a committee that has 2 sophomores, 3 juniors, and 4 seniors. If there…

A: In this question out of 7 sophomores we have to choose 2, Out of 8 juniors, we have to choose 3 and…

Q: Assume that five men and five women are to sit in a row of ten chairs how many ways can these people…

A: Five men and five women are sitting in a row of ten chairs.

Q: Suppose that you must choose three people to meet with a customer. You have nine people to choose…

A: Given data, Total number of people (n)=9 Number of people to meet with a customer (r)=3

Q: A time traveler can take 4 books with him, and he has 98 books to choose from. How many different…

A:

Q: There are 17 students in a class and seven of them will be chosen to go on a field trip how many…

A: It is given that Total number of students n = 17 Students to be selected r = 7

Q: a committe of 5 people is to be chosen from a group of 6 men and 4 women how many committed are…

A:

Q: Suppose you have 11 books and you randomly pick 3 to take on vacation with you. How many ways can…

A: To count the number of possible selections

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.