You have 4 shades of blue apint and 3 shades of red paint. You are paint a room, and wish to use three different colors to paint the walls one color, the moldings another color, and the ceiling a third color. (Using two different shades of blue, for instance, is using two different colors.) How many ways are there to paint a room if at least one shade of blue and one shade of red are used?

Q: 16. You go to Baskin Robins to buy an ice-cream. If you have 3 kinds of cones, 31 flavors, 8…

A:

Q: A Broadway theater has 800​seats, divided into​ orchestra, main, and balcony seating. Orchestra…

A: x= number of orchestra​ seats y= number of main​ seats z= number of balcony seats

Q: During the fall semester a school is offering science courses in physics, biology, and chemistry,…

A: It is given that there are science courses in physics, biology, and chemistry, and humanities…

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: A junior executive looking at his business attire in his closet notes that he has five suits, six…

A: Given, A junior executive has five suits, six shirts, and three pairs of shoes. He is going on a…

Q: Molly is making peanut butter cookies. To make a batch of cookies she needs 3/4 cups of peanut…

A:

Q: At the ice cream shop, there are 21 flavors of ice cream available. How many ways can you select a…

A: According to the combination rule, if r distinct items are to be chosen from n items without…

Q: Mrs. Ruiz has 15 boys and 14 girls in her class. There are 165620 ways to choose a committee to…

A: Given: Number of boys = 15 Number of girls = 14 Number of boys in a committee = 3 Number of girls in…

Q: A sushi restaurant offers a three-course buffet lunch. Each customer must make one selection from…

A: The customer can select 1 item : from the reddish range in 5 ways. from the yellow dish range in 6…

Q: Amy is arranging 11 cans of food in a row on a shelf. She has 4 cans of peas, 1 can of carrots, and…

A:

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: Nine people are going to travel for a party in two cars. The larger has 5 seats, and the smaller has…

A:

Q: Adrian sells handmade puppets for $10 apiece. One puppet gets damaged, so Adrian sells it for $6,…

A: Adrian sells handmade puppets for $10 apiece. One puppet gets damaged, so Adrian sells it for $6,…

Q: 2. Nancy is arranging books on her bookshelf. She has 16 books total. She has 6 reference books, 4…

A: Number of books in total =16 Number of reference books =6 Number of fantasy novels = 4 Number of…

Q: At the Roseville Middle School Spring Festival, Ellen is running the egg-dying station. She needs 5…

A:

Q: Combination. There are 15 technicians and 11 chemists working in a research lab. They need to form a…

A:

Q: In each of the parts below, the coins available are half-dollars, quarters, dimes, nickels, and…

A: This question can be solved using permutation and combination.

Q: a candle company sells individual candles, boxes with 8 candles, or containers with 15 boxes. At the…

A: Given:The number of candles in a box is 8.The number of box in a container is 15.At the beginning,…

Q: There are 64 dogs and cats at the pet store. If one out of every 4 animals is a cat, how many dogs…

A: Given Data: The total number dogs and cats at the pet store is: N=64 Let, The number of cats is x.…

Q: Pizza is available with three kinds of cheese and four toppings. How many different ways can you…

A:

Q: At a deli counter there are 7 sandwiches with meat and 6 vegetarian sandwiches. Carols is at the…

A:

Q: To select a stir-fry dish, a restaurant customer must select a type of rice, protein, and sauce.…

A: From the provided information, The restaurant offers two types of rices, three proteins and seven…

Q: To order a flavored latte at a coffee shop, you have to pick a size, a type of espresso, a type of…

A: Number of ways to choose a size = 3 Number of ways to choose a type of espresso = 10 Number of ways…

Q: My little brother loves the video “hunting game” he got for Christmas. He gets 2 points for…

A:

Q: A restaurant offers a pasta deal where you choose a type of pasta, a sauce, and two additional…

A: Given that the restaurant offers a pasta deal where you choose a type of pasta, a sauce, and two…

Q: How many ways can Susan assign someone to buy​ beverages, someone to arrange for​ food, and someone…

A: Here Given  Susan Has 9 Friends   (Vicki, Luis,​ Maddy, Hank, Rob, Sean, Marie, Roy, and Jeanne)

Q: At the flower shop, Maggie is making a bouquet from asters, dahlias, irises, roses and…

A: Maggie needs to form a bouquet consisting of 9 flowers, taking flowers out of 5 given types of…

Q: A man owns 6 pairs of pants, 7 shirts, 8 ties, and 2 jackets. How many different outfits can he wear…

A:

Q: You have 5 shades of blue paint and 2 shades of red paint. You are painting a room, and wish to use…

A: Given information: The number of shades of blue paint is 5. The number of shades of red paint is 2.…

Q: After gym class you are tasked with putting the 19 identical dodgeballs away into 9 bins. How many…

A:

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

A:

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: Andie has a blue sweater, a red sweater, and a purple sweater. She has a white shirt and a tan…

A: Our objective is to find in how many different ways can she wear asweater and a shirt together.

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: A medical salesperson is to visit the various members of the staff at a clinic. He must see 8…

A: It is given that the sales person must see 8 doctors, 6 physicians assistants, 12 nurses, 3 medical…

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: A boy owns 2 pairs of pants, 3 shirts, 8 ties, and 2 jacket. How many different outfits can he wear…

A:

Q: A school dance committee is made up of 2 freshman, 5 sophomores, 2 juniors, and 5 seniors. How many…

A: Given Data- A school dance committee is made up of: Freshman =2 Sophomores = 5 Juniors = 2 Seniors =…

Q: On a business retreat, your company of 28 executives go golfing. a. You need to divide up into…

A: Solution:   The total number of distinct ways of arranging the letters of the word of length N…

Q: Farmer Brown owns six horses and seven mules. He takes them into the barn where there are five…

A:

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: 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: There are four boys and four girls at a party. In how many ways can they be seated in a row if they…

A:

Q: 725 tickets were sold for a game for a total of $1,100.00. If adult tickets sold for $2.00 and…

A:

Q: A certain car dealership sells two models of cars: Model S and Model V.  Model S comes in 8…

A:

Q: coffee shop offers 10 different types of flavor shots. If customer can choose any number of flavor…

A:

Q: Peg has 6 long-sleeve shirts, 7 short-sleeve shirts, and 4 pairs of pants. (a) How many different…

A: Given data - Peg has 6 long sleeve shirts,7 short sleeve shirts and 4 pair of pants. We have to…

Q: How many senior breakfasts did he prepare?

A:

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

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.