A jar is to be filled with 100 jelly beans. There are five varieties of beans to choose from and we are required to use between 10 and 50 beans of each variety. How many different ways of filling the jar are there?

Q: At a furniture store, there a 4 different sizes of sofas, 7 different colors of fabric , and 8…

A: Given that, No.of  different sizes of sofas = 4 No.of different colors of fabric =7 No.of different…

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: How many ways are there to stack an ice-cream come with 4 scoops if the choices are pistachio,…

A: The choices are pistachio, peach, cherry, walnut, peanut butter, and raspberry. That is 6. I scoop…

Q: How many ways can 2 students be selected from a group of 5 students if order matters?

A: Solution-: We find number of ways 2 students be selected from a group of 5 students if order…

Q: From a club of 25 people, in how many ways can a group of six members be selected to attend a​…

A: In how many ways a group of six members can be selected from a club of 25 people.

Q: There are 2 copies each of 4 different books. In how many ways can they be arranged on a shelf?

A:

Q: an eyewitness to a crime said that the license plate of the getaway car began with the letters Y,B,…

A:

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: 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: Six people are about to enter a cave in a single row. In how many ways could the arrange themselves…

A: Given: Six people are about to enter a cave in a single row

Q: How many ways can all the dogs be lined up for a photograph, if all the dogs of a similar breed must…

A: Hi thank you for the question. As you have requested solution for the last 2 subparts, we'll answer…

Q: A committee of 6 people, with two of the six to be designated chair and vice-chair, is to be…

A: Given : Total number of people = 20 Number of committee member = 6

Q: There are 280 students in 20 classes. If the number of students in each class is  the same, then how…

A: We have no of students..

Q: You have 5 Math books, 2 History books, and 4 Science books. How many ways are there to arrange the…

A: If there are n number of distinct objects out of which r objects are selected and then arranged then…

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

A:

Q: 1. Suppose Ivana has 4 shirts, 3 pairs of pants and 3 pairs of shoes. How many different outfits can…

A: Given: Ivana has 4 shirts, 3 pairs of pants and 3 pairs of shoes. The total different outfits Ivana…

Q: In a group of dogs and their owners, there are exactly 20 heads and 64 legs.  How many dogs are in…

A: Let, x be No of men. y be no of dogs   Men consists of 2 legs and dog has 4 legs.   x+y=20 2x+4y=64

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: How many ways can 12 people line up if Joey and Sally must be next to each other?

A: here given group of 12 people arrange in raw   and arrange around round table

Q: A state makes license plates with two letters followed by four numbers. if no repetitions of the…

A: The license plates must consist of two letters followed by four numbers.

Q: Three members of an organization volunteered to serve as President, Treasurer and Secretary. In how…

A:

Q: Radio stations that are on the west side of a nation have call letters consisting of a K followed by…

A: The first letter is fixed with Z and is then followed by 4 letter( repetition allowed) Then,

Q: A girl has 9 skirts, 4 blouses, and 6 pairs of shoes. How many different skirt-blouse-shoe outfits…

A: 5) Given that the girl has 9 skirts, 4 blouses and 6 pairs of shoes. Total number of ways 9+4+6=19…

Q: Harry has to visit 10 cities. He can visit three in any one day, and the order in which he visits…

A: Combinations: The number of combinations of r items selected from n items is, nr=n!n-r!r! Harry has…

Q: In an apartment complex there are 5 windows in each apartment, and 9 apartment in each floor. How…

A:

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: A softball league has twelve teams. If every team must play every other team once in the first round…

A: Topic: Permutations and combination

Q: A clerk at a bookstore is restocking a shelf of the best-selling novels. He has two copies each of…

A: Part 1: The total number permutations in which 6 books can be arranged is 6! Since there are three…

Q: There are three separate, equal-size boxes, and inside each box there are four separate small boxes,…

A: Here, Number of Big boxes =3 Small boxes: Inside each box there are four separate box.  i.e.  3 x 4=…

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: The newest cars have 12 different accessories and the buyer pays for each one separately.  If a…

A: Given, The newest cars have 12 different accessories A buyer wants to buy four accessories

Q: There are 3 apples, 5 pears and 4 oranges in a basket. If a waiter were to line up these fruits side…

A: There are 3 apples, 5 pears and 4 oranges in a basket. Total fruits = 3+5+4 = 12 n distinct objects…

Q: In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the…

A:

Q: A class of 20 students is seated in a classroom with 5 rows of 4 seats each. How many ways are there…

A: Number of ways in which n students can be divided into k groups of h students is given by,

Q: There are nine boys to every seven girls in an introductory class geology course . If there are 368…

A: Simplification

Q: How many different meals are possible from a menu if you choose one each of 5 appetizers, 4 entrées,…

A: Given data : Number of appetizers= 5 Number of entrees= 4 Number of desserts= 3 Number of beverages=…

Q: From a garden with 6 flower varieties, a bouquet of 3 differer types of flowers is to be picked. How…

A: using permutation and combination in these type of problems.

Q: A dance club needs 3 new members. If there are 5 males and 9 females applicants, in how many ways…

A: Solution

Q: A fishing camp has 15 clients. Each cabin at the camp will accommodate 6 fishermen. In how many…

A: Combination: The number of different selections of ‘r’ elements (order doesn’t matter) from a set of…

Q: Suppose an outfit consists of a shirt, pants, and shoes. If you have 4 shirts, 7 pairs of pants and…

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

Q: A teacher and his eleven students are standing in a single file line waiting to enter the cafeteria…

A: We have given that a teacher and his eleven students are standing in a single file line waiting to…

Q: You baked seven cupcakes of different flavor. In how many ways can you  give two cupcakes each to…

A: Here Given  Total No of cupcakes=7 No of given to each friends=2 No of cupcakes keep with himself=1

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

A:

Q: A bus has 8 vacant seats in the first rows. If 3 additional passengers enter the bus, in how many…

A: For the number of ways of their seating, we need to use combination.

Q: If there were to be 15 boys and 13 girls at a party and the host wanted each to be given exactly…

A:

Q: There are six boys to every five girls in an introductory geology course. If there are 374 students…

A:

Q: If there are five different toy cars, and you want to put fifteen toy cars on the display, how many…

A: Permutation is the measurement of principle counting. It is measure that arrange the data in an…

Q: A university has 338 sections of Math 01. If 45 students are enrolled in each section, how many…

A: It is given that there are 338 sections of Math 01. The number of students enrolled in each section…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.