new dormitory is to be constructed.  There will be three types of rooms: single rooms which accommodate just 1 student per room, double rooms which accommodate 2 students per room, and triple rooms which accommodate 3 students per room.  The dorm will contain 151 rooms and accommodate 262 students. Further, there will be 20 more double rooms than single rooms.  Find the number of each type of room.

Q: A bag contains 3 lemon, 2 cherry, and 6 grape candies. A handful of 4 candies is grabbed from the…

A: At most 1 grape candy means 0 or 1 grape candy. There are 6 grape candies and (3+2)=5 non-grape…

Q: Suppose Pat has eight shirts and four pairs of pants. How many different outfits  can Pat make by…

A: The person has 8 shirts and 4 pairs of pants and he can make one outfit by combining one shirt with…

Q: Ethan owns 8 pairs of pants, 4 shirts, 4 ties, and 3 jackets. How many different outfits can he wear…

A: The above example is an example of a combination. we have to find different combinations of outfits.

Q: A combination has 4 characters.  There are 2 letters and 2 numbers.  The numbers must be 0-9.  how…

A: Given : There are combinations of 4 characters. There are 2 letters and 2 numbers.

Q: Elizabeth's tablet has a combined total of 20 apps and movies. Let x represent the number of apps…

A: Given, Elizabeth's tablet has a combined total of 20 apps and movies. Let xrepresent the number of…

Q: Sophie is working at a hair salon and building a tool kit. There are 8 hair dryers and 10…

A:

Q: A student is to answer 12 out of 15 questions on an exam. How many choices does he have?

A: The total number of questions in the exam is 15. The student has to answer 12 out of 15 questions.…

Q: Kisses and Lovely are setting up tables for the birthday party of their friend at the barangay…

A: Kisses and Lovely are setting up tables for the birthday party of their friend at the barangay…

Q: Set B pages 393-396, 397-400 A 4-foot board is cut into pieces that are foot in length. How many…

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

Q: Claire spends most of her day reading on the beach during her vacation. Use the clues below to…

A: This is a simple equation based problem. I used substitution method to solve the above problem.

Q: Mr. H has a collection of 500 vessels. In how many ways can he name his favorite and second favorite…

A:

Q: In a batch of 500 high school students, there are 252 students who own a laptop, 176 students who…

A: Here we can use the formula nU = nA+nB-nA∩B+nA∪B'

Q: a law firm has 8 male and 6 females lwayers. a committee of 5, two male lawyers and 3 female…

A: The objective of the question is to find out the number of possible committees that can be formed…

Q: Amy, Jade, Jhune and Renier have varied favorite colors among red, blue, green, and orange. No…

A: We used three clues given in the question.

Q: a law firm has 8 male and 6 females lwayers. a committee of 5, two male lawyers and 3 female…

A: The objective of this question is to find out the number of possible committees that can be formed…

Q: Marissa's cycle repair shop fixes normal bicycles and tricycles. Marissa had to assemble a number of…

A:

Q: There are 6 boys playing soccer. 3 boys go home. Then 1 more boy goes home. How many boys are there…

A: Given that there are 6 boys playing soccer, 3 boys go home then 1 more boy goes home. We have to…

Q: Johnny has 54 apples and 89 grapes. He gives half of his apples to Samantha, who already had 5. Then…

A: Given,            Johnny has 54 apples and 89 grapes. He gives half of his apples to Samantha,…

Q: A boy owns 7 pairs of pants, 2 shirts, 20 ties, and 7 jackets.  How many different outfits can he…

A:

Q: The Art Department at AUM has three painting from Mike, five by Amy , and 3 by Jack.  In how many…

A:

Q: Sherazan must make a dental appointment on Tuesday or Thursday. The dentist has 10 appointment times…

A:

Q: You are purchasing a box of donuts to share with your coworkers. Each box contains 12 donuts. There…

A: Number of 12-combinations of a set of 4 elements is:

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

A:

Q: A theater has 22 rows of seats. The first row has 17 seats, the second row has 21 seats, the third…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: a card store received a shipment of 12 cartoons of sports cards . Each cartoon contains 20…

A:

Q: A large auditorium has 90 rows of seats. The first row has 50 seats, and each succeeding row has 5…

A:

Q: After a service call by a plumber, the company follows up with a survey to rate the service and…

A: For yes/ no type questions:

Q: Your car seats 5 people, including the driver. You have 8 friends who all need you to drive them…

A:

Q: A boy owns 5 pairs of pants, 7 shirts, 3 ties, and 3 jackets. How many different outfits can he wear…

A: Given that  A boy owns  5 Pairs of pants 7 shirts 3 ties 3 jackets

Q: A party room has a circular table with 12 seats. A group of 4 people enter the room. How many…

A: In a circular table with n seats,  there are (n-1)! ways ofoccupying the seats

Q: books are arranged in a display that has 4 rows. each row has one more book than. the row above it.…

A: Books are arranged in a display that has 4 rows. Each row has one more book than the row above it…

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.