(a). Three boys and three girls are seated at the round table. How many different arrangements are possible if the girls and the boys must be seated alternately?

Q: A group of nine people are attending the movies together.   (a) Two of the nine insist on sitting…

A:

Q: Four married couples have bought 8 seats in a row for a concert.  In how many ways can they be…

A: If each couple sits together, we can think of each couple as 1 unit. So there are 4 units to be…

Q: A family with three children are to pose for a family picture in a row. la) In how ways can they be…

A: Given Information: A family with three children are to pose for a family picture in a row.  (a) In…

Q: Grace loves to eat salad how many salads can she put together if she can choose one from each of the…

A: In this question, we need to find how many salads can grace put together.

Q: 8. A school class is holding a raffle and 10 prizes are to be awarded. One hundred twenty people…

A:

Q: A class has 32 students.  18 have hats, and 17 do not wear glasses.  5 students wear glasses but do…

A: We use ven diagram to solve this problem.

Q: Donald is making a salad at Sweet Tomatoes.  His salad can consist of just lettuce, or he can add…

A:

Q: 6. You have a pool of 9 women and 16 men, and you need to form a 12-member team made up of six men…

A: Hi! Thank you for the question. AS per the honor code, we are allowed to answer only one at a time…

Q: A girl can take 3 books from her school library and there are 10 books of her interest in the…

A: Given is ; There are 10 books of her interest and she can take 3 books from her library Calculation…

Q: III. 50 people were surveyed about whether they like the ice cream flavors vanilla and strawberry.…

A: Total number of people= 50 Total number of people who liked vanilla = V= 20 Total number of people…

Q: Transportation In a train yard, there are 12 flatcars, 10 tanker ears, 15 boxcars, and 5 livestock…

A: Given : In a Train yard Flatcars=12 Tanker cars = 10 Boxcars =15 Livestock cars =5

Q: a) The ice creaM shop offers 4 flavors. You order a double-scoop cone. In how Many different ways…

A:

Q: involving the cans of cola in a cooler. For this problem, assume the cooler contains 36 cans, 20 of…

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Q: You were tasked to take charged of the auditions for the female part of the stage play. In how many…

A: Let us analyze this problem for a bit. A hopeful does not care if she is selected first, second or…

Q: twenty tickets are entered into a raffle. 1st prize receives $100;2nd prize receives $25;3rd prize…

A: In theory of combinatorics, the way of selecting r objects from n objects with regard to the order…

Q: 700 people went to the amusement park. 500 of them went on a roller-coaster, 100 of them went to the…

A: Let R=roller coaster  H=Haunted house W=water slides S=total 700 people Given, 2 people went on all…

Q: 1. Your brother is ordering 5 pizzas for the family. There are 18 different kinds of pizza. How many…

A:

Q: . Beth has 8 friends. How many ways can she invite one or more of them to dinner?

A:

Q: How many ways can a group of five boys and five girls be seated in a row of ten seats if boys and…

A: Here we have to find no. Of ways in the given problem.

Q: Committee: The Student Council at a certain school has eight members. Four members will form an…

A: The student council at a certain school has eight members. Four members executive committee…

Q: 30. The number of floats in the last Panagbenga Festival is about 50. This year, it is expected that…

A: here given , The number of floats in the last Panagbenga Festival is about 50. This year, it is…

Q: You have 4 shades of blue apint and 3 shades of red paint. You are paint a room, and wish to use…

A: Let a, b, c, d denote the 4 shades of blue and x, y, z the 3 shades of red. The different…

Q: Pizza House offers three different​ salads, two different kinds of​ pizza, and three different…

A:

Q: 8. A school class is holding a raffle and 10 prizes are to be awarded. One hundred twenty people…

A: We will answer the first three sub questions as per our guideline. Please resubmit the other…

Q: You are purchasing 16 bagels from the bagel store and only the type of bagel matters (so bagels of…

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

Q: In a city, the bus route numbers consist of a natural number less than 100, followed one of the…

A: In a city, the bus route numbers consist of a natural number less than 100, followed one of the…

Q: A group of ten people are attending the movies together. (a) Two of the ten insist on sitting…

A: Given that, a group of ten people are attending the movies together. a) Given that, two of the ten…

Q: 4. It is your little brother's birthday, and he has invited 5 of his friends to come to his party.…

A:

Q: In how many ways one can select a group of three students out of 6 boys and 4girls. If a group…

A: Given : Number of boys = 6 Number of girls = 4 we have to select a group of three students a) two…

Q: 6 people consisting of 3 couples are seated in a row of 6 chairs to take group pictures. (a) In how…

A: in following ways they can be seated

Q: Seven women and nine men are on the faculty in the mathematics department at a school. How many ways…

A: Given : In a Mathematics department of school ; No. of women = 7 No. of men = 9 Sample size (n) = 6…

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: Q2: According to a well-known legend, the game of chess was invented many centuries ago in…

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Q: (b) A class of 18 students is divided into 3 groups of four students and 2 groups of three students.…

A: As per given by the question, A class of 18 student is divided into three groups of four student and…

Q: - In how many ways can you arrange the letters in the word RHOMBUS?

A: Solution: 1. The word RHOMBUS has 7 letters.

Q: a dinner gathering. In how many ways can the host (one of the 12) arrange his guest around a dining…

A: To find:  1.Number ways can the host arrange his guest around a dining table. 2.Number of ways three…

Q: 10. A charity benefit is attended by 25 people and three gift certificates are given away as door…

A: The permutation is the process which helps to understand the number of arrangements of data in an…

Q: Magellan has decided to make party baskets for the fund raiser. Balloons are sold in bags of 20,…

A:

Q: From a group of 10 men and 12 women. How many committees of 5 men and 6 women can be formed?

A:

Q: 4. Beverly sells mangoes. She sold half her mangoes plus half a mango last Monday. Then she sold…

A: Let the number of mangoes B has be x.

Q: In a mathematics​ class, students received an A on the third​ test, which is ​% of the students who…

A: Step 1

Q: A school class is holding a raffle and 10 prizes are to be awarded. One hundred twenty people enter…

A: Solution is in next step

Q: Five men and five women line up at a checkout counter in a store. In how many ways can they line up…

A: Consider the given: According to Question: Number of ways can five men line up at the counter =…

Q: At a meeting between coworkers, the eight participants sit on a round table facing the beach. There…

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

Q: 2. A customer at a pizza shop wants to order a pizza. A pizza consists of choosing a crust, a type…

A: Given: The pizza has 4 types of crust, 5 types of cheese, and 20 toppings

Q: 02)• 20 students and the dean came to the cinema and want to sit in the same row, in which there are…

A: Given that, 20 students and the dean came to the cinema and want to sit in the same row, in which…

Q: At the ice cream shop, there are 19 flavors of ice cream available. How many ways can you select a…

A: Given,Total no.of flavours=19

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.