There are four different trails to the top of a mountain. In how many ways can a person hike up and down the mountain if he must take the same trail both ways? he can, but doesn’t need to, take the same trail both ways? he does not want to take the same trail both ways

Q: if there are no restrictions? if Holly and Sam cannot sit together?

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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: student needs 6 more classes to graduate. If she has met the prerequisites for all the classes, how…

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Q: The director of the school play has to assign 5 lead roles. If the roles are being chosen from a…

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

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Q: There are 16 seniors and 20 juniors in a particular social organization. In how many ways can 2…

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Q: In a family of cats, there are 2 un-cool cats for every 3 cool cats. If these cats have 120 paws…

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Q: Suppose for your afternoon snacks, you may select juice, milk tea, or soda for your drinks. You also…

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

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Q: There are three boys and three girls at a party. In how many ways can they be seated if they can sit…

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A: Given: Total friends = 5 Number of friends that could be brought along = 2

Q: In a certain jungle, there are three tribes: Tribe T, Tribe L, Tribe X. Members of Tribe T always…

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

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Q: You have 7 math books and 7 history books to put on a shelf with five slots. In how many ways can…

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Q: At Mr. Furry's Dance Studio, every man must dance the last dance. If there are six men and nine…

A: Given that there are six men and nine women and every man must dance the last dance. Here total…

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: There are 360 students and 2/3 went to a field trip. Of these students, 40% were wearing t- shirts…

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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: If the first chapter of a certain book is 30 pages long and makes up 10% of the book, how many pages…

A: Given that, the first chapter of a certain book is 30 pages long and makes up 10% of the book.

Q: you had a box of five different kinds of fruit and you could choose 2, you might get an apple and an…

A: Given that  Number of types of fruits (n) = 5 Number of fruits we could choose = 2   We know that…

Q: Colin has 9 cd’s in his carrying case – two John Tesh, three Michael Jackson, and four Beatles. How…

A: Given: Number of cds = 9 Number of John Tesh cds = 2 Number of Michael Jackson = 3 Number of Beatles…

Q: If a plumber and a helper can install a water heater and a half in a half day, then how many water…

A: According to the given information it is required to find the number of water heaters that 20…

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Q: On Monday, tom worked 2 hours and Sylvester worked 3 hours and they made a total of 23 traps. On…

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

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Q: There are 4 routes from A to B, 8 routes from B to C, and 12 routes from C to D. How many routes are…

A: Given : The number of routes from A to B is 4 The number of routes from B to C is 8. The number of…

Q: How many ways are there to go from B to D?

A: here given  A boy lives at B and wants to go to school at D. From his home B he has to first reach C…

Q: To fill a number of vacancies, the personnel manager of a company has to choose three secretaries…

A: The number of ways a company has to choose three secretaries from among ten applicants can be done…

Q: f any arrangement of letters is considered a word, and there are 21 consonants and 5 vowels to…

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Q: How many possible license plates can be issued with two letters followed by three numbers?

A: The state issues license plates consisting of letters and numbers. There are 26 letters and the…

Q: A student is to answer 10 out of 13 questions on an exam. (i) How many choices has he? (ii) How many…

A: Note: Hey, since there are multiple subparts posted, we will answer first three subparts. If you…

Q: remy's bedroom has two doors leading into the hallway. His house has four doors leading to the…

A: Here Jeremy's bedroom has two doors leading into the hallway. His house has four doors leading to…

Q: Marissa's calculus​ course, attendance counts for 5​%of the​ grade, quizzes count for 15​% of the​…

A: Given data,   Weightage (w) score (x%) x*w attendance 0.05 100% 5 % quizzes 0.15 89% 13.35 %…

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

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Q: In how many ways can Coy drive from Caroline's city to Karl's city and return, going through Janry's…

A: Consider the following diagram to visualize the situation, As Coy begins the journey from…

Q: Twelve people need to be photographed, but there are only five chairs. (the rest of the people will…

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Q: A) 15 people are playing soccer, only 3 people know how to be a goalkeeper, how many ways are to…

A: INTRODUCTION :  probability: If a random experiment or a trial results in 'n' exhaustive, mutually…

Q: If there are 3 roads from Town A to Town B and 4 roads from Town B to Town C, in how many ways can…

A: there are 3 ways to go from A to B  4 ways to go from B to C  3 ways to go from C to B as we can not…

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

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

Q: A southeast regional salesman has eight destinations that he must travel to this month: Atlanta,…

A: Given : A southeast regional salesman has eight destinations that he must travel to this month:…

Q: A history teacher gives a 20 question true-false exam. And how many ways can the test be answered if…

A: Fundamental principal of counting : if a  thing can be done in m ways and another thing in n ways ,…

Q: There are only seven seats in a van. One of the seats is modified to fit only a baby and one is the…

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Q: A, B, C, and D are going to ride in A’s car to go to the mall. But only A and C know how to do drive…

A: Given, The number of individuals is 4 The individuals are A, B, C and D. The number of front seats…

Q: 3. Marty is a bookworm and he has various collections of novels, series and other story books. If he…

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Q: A donut shop has 5 varieties of donuts and we want to order 10 donuts. But today, among their 5…

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Q: You and 3 friends are moving into a 4-bedroom house and need to decide who gets which room. How many…

A: There is total 4 persons.

Q: There are 3 ways to get from Town A to Town B, 4 ways to get from Town B to Town C, and another 5…

A: There are 3 ways to get from Town A to Town B. 4 ways to get from Town B to Town C. and another 5…

Q: It’s the first day of summer camp, and the counselors are trying to figure out where one of the…

A: Given: There are four beds available in Cabin #1, five in Cabin #2, and just one in Cabin #3. To…

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.