A birthday cake is to have two layers of cake separated by a layer of icing, with another layer of icing on top. There are 5 kinds of cake the chef knows how to make, and she may use either two different kinds or the same one twice for the two cake layers. The chef recipes for 3 different icings, and she will use two different recipes, one for eac

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

A: Let a, b, c, d, e be the different kinds of cake known. Let x, y, z be the 3 different types of…

Q: In a football league, each team plays each of the other teams twice during the season, once at home…

A: Here we will going to use basic concept of Combination.

Q: A college freshman must take a science course, a computer science course, and a mathematics course.…

A:

Q: For each situation below, identify whether it is a permutation or combination problem and then find…

A: Permutation relates to the act of arranging all the members of a set into some sequence or order.…

Q: Apple decided to give an apple watch to the first person in line, an iPhone to the second person in…

A: From the given information, Apple decided to give apple product to all three persons who stand up in…

Q: A woman has ten skirts and five blouses. Assuming that they all match, how many different…

A:

Q: In an art gallery there are 10 paintings to be hung on a wall, but 5 of which must be hung in a row.…

A: There are 10 paintings in an art gallery. Of which 5 paintings must be hung in a row.

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

A:

Q: A small high school has 30 seniors, 20 juniors, and 10 sophomores. If 3 students are chosen from…

A: A small high school has 30 seniors, 20 juniors, and 10 sophomores. If 3 students are chosen from…

Q: A restaurant offers a menu with 5 appetizers, 5 main dishes, and 4 desserts.  If Zoey is low on cash…

A:

Q: one family has comfortable children, with four daughters and two sons from a village of 1000 houses,…

A: As per given by the question, one family has comfortable children's with four daughter and two son…

Q: At a certain French restaurant, a multi-course meal is offered, where patrons can choose from…

A:

Q: A student club consists of 10 freshmen and 8 sophomores. How many different four-person committees…

A: A student club consists of 10 freshmen and 8 sophomores.

Q: If a team of four players must be made from eight boys and six girls, how many teams can be made if…

A: 1. There are eight boys and six girls, totally there are 14 players. A team of four player. The…

Q: When an ice cream shop was founded, it made 37 different flavors of ice cream. If you had a choice…

A: Given- When an ice cream shop was founded, it made 37 different flavors of ice cream. If we had a…

Q: A sum of $1300 is divided amongst P,Q,R and S such that P share/Q share = Q share / R share=R…

A:

Q: An ice cream store has 30 flavors to select from. A customer who is a connoisseur of ice cream wants…

A: We have to select three different flavors from a ice cream store which has 30 flavors. Since, here…

Q: A roller coaster has 3 trains with 8 rows per train. Riders stand in rows of 4, for a total of 32…

A: A fraction is a number in the form xy (where x and y are both integers and y≠0). In the above number…

Q: Six friends are taking a film history course and, because they have procrastinated, need to view…

A: Given information Six friends have a total of three DVD players in different dorm rooms and If each…

Q: You and 3 friends are moving into a new apartment-style dorm. The dorm has 3 bedrooms, one with two…

A: There are totally 4 members. These 4 members must be arranged in 3 bed rooms. One bedroom has two…

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

A:

Q: At a local restaurant, a dinner special consists of choosing a salad, an entree and a dessert. If…

A: If there are 3 choices for salad, 6 choices for the entree, and 4 choices for dessert. At a local…

Q: Ethan is at a sandwich shop and is looking at the combo meal, which includes a sandwich, a choice of…

A:

Q: The owner of a stereo store wants to advertise that he has many different sound systems in stock.…

A: The owner of a stereo store wants to advertise that he has many different sound systems in stock.…

Q: I am going to give my 4 brothers and 1 sister some candies. I have a box of 48 similar candies, and…

A: given that :Since Total number of confections are 48 All out number of siblings and sister are 4+1…

Q: The Simple Machine Company makes Widgets, Gadgets, and Gizmos out of pulleys, wedges, and levers.…

A: Consider the table as follows   Widgets (x) Gadgets(y) Gizmo(z) availability pulley 2 2 1 20…

Q: The Enormous State University History Department offers three courses, Ancient, Medieval, and Modern…

A: Given : Equations is givens

Q: A certain school has 3 desktop computers for every 4 laptop computers, and it has 70 computers…

A: Given : A certain school has 3 desktop computers for every 4 laptop computers and it has a total…

Q: In a class of 40 students, all even numbered students opted to take Physics, those whose numbers are…

A:

Q: A basketball fan has a pair of tickets to 6 different home GAMes of the Los Angeles Lakers. If the…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: How many children are there in a family wherein each girl has as many brothers as sisters, but each…

A: Let assume Number of sister = x Number of brother = y

Q: A teacher has 24 colored pencils and 18 pictures to be placed in groups with the same number of…

A: Question 3:             It is given that a teacher has 24 colored pencils and 18 pictures. The…

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 3. The number of types…

Q: A chain of convenience stores has 4 warehouses and operates 35 retail outlets. In how many different…

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

Q: Jodi delivers 54 newspapers on Saturday and 78 newspapers on Sunday she makes bundles of 6…

A: Given: Jodi delivery newspaper on Saturday =54 Jodi delivery newspaper on Sunday =78 She makes…

Q: semester

A: We will find how many different possible schedules are there for Felicia to choose from.

Q: The Little Twelve Basketball Conference has two divisions, with nine teams in each division. Each…

A:

Q: If you have six books, but there is room for only four books on the shelf, in how many ways can you…

A: From the given information, n=6 and r=4.

Q: How many breakfast meals consisting of a fruit, a sandwich, and a drink are possible if one can…

A:

Q: At the restaurant i 23 Σ π, they have 11 appetizer, 6 soup, 6 entree, and 24 dessert options.  How…

A: Given: There are 6 soup, 11 appetizer,  6 entree and 24 dessert options at the restaurant.

Q: The Shepard family--Jake, Jena, Jamie, and their mother--ordered two pizzas. Jake ate 2 3 of one…

A: Given, Number of pizzas ordered = 2 Jake ate = 23 of one pizza Jenna ate = 12 of a pizza Jamie ate =…

Q: A room with X full rows of chairs has every chair filled with a person. If there are y people…

A:

Q: If I go into an ice cream parlor, and I have the choice of having one of 10 different flavors, with…

A: Given information- No. of different flavors available at an ice cream parlor = 10 No. of different…

Q: A philanthropist, on his free day, seeks to visit an orphanage from the seven orphanages he supports…

A: Given information No of orphanages = 7 No of elementary school = 10 No of care homes = 8

Q: A boy owns 2 pairs of pants, 7 shirts, 4 ties, and 5 jackets. How many different outfits can he wear…

A:

Q: How many ways are there to stack an​ ice-cream cone with 4 scoops if the choices are   a.…

A: For flavours must be different then once used flavour can't be used next time. So in first stack we…

Q: At the restaurant i 23 Σ π, they have 8 soup, 21 appetizer, 8 salad, 10 entree, and 20 dessert…

A: At the restaurant i 23 Σ π, they have 8 soup, 21 appetizer, 8 salad, 10 entree, and 20 dessert…

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.