Three actions are to be performed in a definite order. There are four possibilities for the first action; corresponding to each of these possibilities are five possibilities for the second action; and corresponding to each of these possibilities are two possibilities for the third action. How many possibilities are there altogether for the three actions?

Q: A fleet of nine taxis is to be dispatched to three airports in such a way that two go to airport A,…

A: Given, A fleet of 9 taxis is to dispatch to the three airports A, B, and C also, 2 go to A, 6 go to…

Q: In a certain class there are a total of 45 majors in mathematics, 15 majors in philosophy, and 5…

A: Topic = Set theory

Q: After a day of skiing a family of six washes all of their ski-wear including their gloves. The next…

A:

Q: 16. A teacher will ask the first student that arrives to class to hand out papers, the second…

A: Given We have 16 students in the class  A teacher will ask the first student that arrives to class…

Q: 1 red, 1 blue, 1 black, 1 yellow and 1 white car are all waiting at the traffic lights behind each…

A:

Q: Mr. Jones has 10 books that he is going to put on his bookshelf. Of these, 4 are Math books, 3 are…

A: Given:- total books =10 maths books =4 Chemistry books =3 history books =2 song lyric book =1

Q: If there is a bird in every branch, there will be an excess bird not on the branch but if there will…

A: Here, it is given to us that: There is a bird for every branch, and if each bird sits on one branch…

Q: Assume that she has 4 possible destinations: Utah, New England, Oregon, and Colorado. There are 4…

A: The objective of the problem is identified below: From the given information, there are 4 possible…

Q: Each student at State University has a student ID number consisting of four digits (the first digit…

A: First digit filled with 9 ways since 0 does not occur Second digit is filled with 10 ways  Third…

Q: There are  12  European cities that Linda would eventually like to visit. On her next vacation,…

A:

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

A:

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

A: Need to find correct tribe for given statement

Q: A true-false quiz contains six questions. In how many ways can a student answer the questions if the…

A: It is given that the quiz has 6 true false questions.It is also given that the student has answers…

Q: You have a four letter string, where each of the five vowels has to be followed by a consonant,…

A: According to the given information, it is required to find the possible number of strings of 4…

Q: Mr. Jones has 10 books that he is going to put on his bookshelf. Of these, 4 are mathematics books,…

A: Given: Number of types of books=4 Number of mathematics books=4 Number of chemistry books=3 Number…

Q: In how many ways can a group of five girls and five boys be lined up so that: (a) all the girls…

A: Permutation: A permutation of a set is defined as an arrangement of its members into a sequence or…

Q: Each student at State College has a student I.D. number consisting of seven digits (the first digit…

A: no.of digits ( 0 to 9)=10no.of letters(A,B,C,D,E)=5

Q: Seven out of every ten monkeys in a zoo are smarter than the zookeepers. If there are 40 monkeys in…

A:

Q: Each student at State College has a student I.D. number consisting of five digits (the first digit…

A:

Q: How many strings of four decimal digits a) do not contain the same digit twice? b) end with an even…

A:

Q: Gina runs every 4 days, cycles every 16 days, and jogs every 12 days. If she did all three…

A:

Q: Suppose there are three different farmers collecting eggs from a hen house. The amount of eggs in…

A:

Q: Each student at State College has a student I.D. number consisting of eight digits (the first digit…

A:

Q: how many ways can 5 textbooks, 3 coffee table books and 2 novels be arranged if the textbooks must…

A: This question is from permutation We have to calculate, in how many ways 5 textbooks, 3 coffee table…

Q: The public library has volunteers re-shelve books after they’ve been returned. When Lisa arrives to…

A: If there are a number of items in type 1 corresponding to that there are b number of items in type…

Q: For the new fall season, a network president has 11 shows in development, and 8 openings in the…

A: The network president has 11 shows in development . There are eight openings in the prime time…

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: Each student at State College has a student I.D. number consisting of 5 digits (the first digit is…

A: Given: Student ID consists of 5 digits and 3 letters. It means that total characters in student ID…

Q: history teacher gives a 14-question true-false exam. In how many ways can the test be answered if…

A:

Q: In a village out of 200 people it was found that 55 people are infected from Malaria, 72 people are…

A: Solution: From the given information, 55 people are infected from Malaria, 72 people are infected…

Q: A group of 10 people consists of 2 boys, 3 girls and 5 adults. In how many ways can a team of 4 be…

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

Q: Each student at State College has a student I.D. number consisting of eight digits (the first digit…

A:

Q: 20 people have volunteered for a 5-person neighborhood advocacy committee. 13 of them are homeowners…

A:

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

A:

Q: Spider has one sock and one shoe for each of its 8 legs. In how many different ways can the spider…

A: There are 8 socks and 8 shoes.

Q: A committee of 5 consisting of 3 girls and 2 boys is to be chosen from a class with 15 girls and 10…

A: Given: Total Number of Girls=15Total Number of Boys=10Commitee required 5 candidate in whichNumber…

Q: Suppose that Ten service customers need service call and the maintenance worker can only service…

A: Based on the information, the dispatcher cares who serviced first, second and third. In this…

Q: A student is told to work any 8 out of 15 questions on an exam. In how   many different ways can he…

A: He will pick a group of questions. The arrangement will not matter, so we will use the combination…

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: A student taking an examination is required to answer exactly 10 out of 15 questions. in how many…

A:

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: How many different 4​-person teams​ (order does not​ matter) can be put together from a group of 27…

A: We have to choose 4 people from 27 persons and the order does not matter. So we will use the…

Q: In a group of 35 music students, 16 students play an instrument, 16 students sing, and 19 students…

A: In the group of 35 music students, 16 students play an instrument, 16 students sing, and 19 students…

Q: suppose that five service customers need service call and the maintenance worker can only service…

A:

Q: number in Z+is written on the back of each of three cards. The numbers are not necessarily different…

A: This is a puzzle and we will solve using the concept of  basic maths

Q: 2) How many elements are in the union of 5 sets if the sets contain 10,000 elements, each pair of…

A: Given that there are 5 sets and sets contains 10,000 elements, each pair of sets has 1000 elements,…

Q: Suppose that a group of 150 students have joined at least one of the chat rooms: one on auto racing,…

A: We want to find n(A⋂B)= ?

Q: a committe of 5 people is to be chosen from a group of 6 men and 4 women how many committed are…

A:

Q: We are making 5-letter words from the set of letters a, b, c, d, e, f..., in such a way that we have…

A: Here we will use permutation /arrangement and combination / selection  Number of way r object can be…

Q: Among the eight nominees for two vacancies on a school board are four men and four women. How many…

A: Solution: It is given that there are 8 nominees for two vacancies on a school board. There are 4…

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.