You have 5 shades of blue paint and 2 shades of red paint. You are painting 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 your room if at least one shade of blue and one shade of red are used?

Q: Helen wants to buy a bunch of flowers. There are five types of flowers available, namely roses,…

A: There are 5 types of flowers. 16 flowers have to be picked with the only restriction being that no…

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

A:

Q: In a class there are 30 female students and 20 male students. A committee of four students need to…

A: There are 30 female and 20 male students.

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: 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: There are 12 cans of fruit and 8 cans of vegetables on a shelf at the food pantry, and you are a…

A:

Q: group of 27 people, made up of adults and children, visited a park. Adult admission to the park is…

A:

Q: Scott has a bag of candies. 2/5 of the candies are red. 3/10 of the candies are green. If there are…

A: Given , In a bag Total Red Candies=12 2/5 of candies are red. And 3/10 of candies are green. We have…

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: 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: a teacher wants to give pizza to her students and each student can eat 1/4 of a pizza. if there are…

A:

Q: A Broadway theater has 500 seats, divided into orchestra, main, and balcony seating. Orchestra seats…

A:

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

A:

Q: You have 3 science books, 2 language books, and 4 philosophy books. In how many ways can they be…

A:

Q: At Wingstop, customers ordering a family meal can choose 4 different wing flavors. If Wingstop has…

A: Given problem is : At Wingstop, customers ordering a family meal can choose 4 different wing…

Q: You have 19 pieces of candy to distribute to 7 people. How many ways are there to distribute the…

A: Total number of pieces of candy is 19. Total number of person is 7.

Q: You have 8 DVDs to place on a shelf, but you only have room for 6 of them. How many different ways…

A: Given,no.of DVDs=8no.of rooms=6

Q: Charles has eight different winter scarves, and he wears three at a time. How many different ways…

A: Given that       Charles has eight different winter scarves and he wears three at a time  We have to…

Q: At a dinner party, 6 men and 6 women sit in a round table. In how many ways can they sit if Bob,…

A: Number of ways to arrange N person around the round table is (N-1)!. Here, there are 6 men and 6…

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: A sixth grade class is having a pizza party. The teacher ordered 5 cheese pizzas, 5 pepperoni and 5…

A: Fractions are used to symbolize a part of a whole.

Q: A man owns 8 pairs of pants, 15 shirts, 12 ties, and 3 jackets. How many different outfits can he…

A: Given he has 8 pairs of pants, 15 shirts, 12 ties, and 3 jackets

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

A:

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

A:

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: Hosea is given $100. Each day, he gains 1% on the total dollar amount he has, then he loses 1% of…

A:

Q: In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least…

A:

Q: One batch of pink paint uses 2 cups of red paint and 7 cups of white paint. Mai made a large amount…

A:

Q: he admission fee for a Fairfax basketball game is $5 for students and $7 for adults. At one of the…

A: The admission fee for a Fairfax basketball game is $5 for students and $7 for adults. At one of the…

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: A complete meal is composed of 1 cup of rice, 1 viand, 1 glass of drinks and 1 dessert. If there are…

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: there are five action,three drarma, and four comedy films at a local mall, if phoebe goes to this…

A: The total number of films in a mall are (5+3+4)=12. Or  Using combination, there a total of 12…

Q: A large box of pencils contains 45 pencils. A small box of pencils contains 25 pencils. How many…

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

A:

Q: A Broadway theater has 400 seats, divided into orchestra, main, and balcony seating. Orchestra seats…

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: A class of 15 students needs to elect a class president, vice president, treasurer, and secretary.…

A: Consider the given information. The class have 15 student and there are four position as given in…

Q: You are planning to plant one durian, one rambutan, one mango and one avocado tree in your garden.…

A: Given that  Plants need to plant Types available in nursery Durian = 1 Durian = 2 Rambutan =…

Q: I have nine books and have room to display only four of them at a time on my bookself. how many…

A:

Q: How many ways can you prepare this cupcake?

A: HERE GIVEN You are decorating a chocolate cupcake to give to your friend, and you can choose from…

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.