b) 1 red, 1 blue, 1 black, 1 yellow and 1 white car are all waiting at the traffic lights behind each other. In how many different ways can they be waiting if the black car and only the black car is between the white and yellow cars?

Q: a blood​ drive, 6 donors with type O+ ​blood, 5 donors with type A+ ​blood, and 2 donors with type…

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: 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: Assume that you have a committee of 12 members, made up of 3 men and 9 women. In how many ways can…

A: We have to find given probability..

Q: Assume that there are 9 girls and 8 boys in the neighborhood club, and a team of 5 is to be…

A: As there are 9 girls and 8 boys now if a team of 5 is to be selected.1) Number of different teams…

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

A:

Q: c) There are 5 airplanes ready to depart. Runway A and runway D are available. How Many ways can 2…

A: We Know that there are 5 airplanes ready to depart. Runway A and runway D are available. We have to…

Q: Let [A1, A2], [B1, B2], [C1, C2] be 3 married couples who attended a concert.  In how many ways can…

A: Permutation: A permutation is an arrangement of objects in a definite order. Let n is the total…

Q: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

A: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

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 a police departmets there are 7 policemen. If there are 7 districts that should be on patrol, how…

A: Given that total policemen, n= 7 And districts, r= 7

Q: A circular table with 10 chairs must be occupied by 5 boys and 5 girls. How many ways can they be…

A: First we fix the alternate positions of the girls Five girls can be seated around the circle in…

Q: 9. There are 5 different roads from City A to City B and 3 different roads from City B to City C. In…

A:

Q: 2. How many different committees of 4 members can be formed from a group. with 7 seniors and 6…

A: Permutations is the collection of items or elements arranged in a different way with ordering where…

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: A computer password must be 3 letters followed by 5 digits (0 through 9). How many different…

A: Note: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 1. If there are two ways to go to Pampanga from Manila and three ways to go to Bataan from Pampanga…

A: Manila to Pampanga : 2 ways Pampanga to Bataan : 3 ways From Batana to La Union : 5 ways     in how…

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: Assume that there are 3 routes from chicago to New york, 5 routes from New York to san fransisco,…

A:

Q: Assume that there are 8 girls and 12 boys in the neighborhood club, and a team of 6 is to be…

A: Given information: Number of girls, g = 8 Number of boys, b = 12 A team of 6 is to be selected. It…

Q: In a certain office, 1/3 of the workers are women , 1/2 of the women are married and 1/3 of the…

A:

Q: Assume that there are 11 girls and 9 boys in the neighborhood club, and a team of 8 is to be…

A: It is the question of permutation and combination. And the whole solution is shown below.

Q: A Convener and a Secretary are to be chosen from group of people consisting of 50 people. Explain…

A: i) We can select A as Convener in only 1 way. We can select Secretary from (50-1)=49 people in 49…

Q: In how many ways can four English books, three statistics books, three chemistry books and two…

A: Number of English books = 4 Number of statistics book = 3 Number of chemistry book = 3 Number of…

Q: Suppose that a department contains 10 men and 18 women. How many ways are there to form a committee…

A: The order of the men/women is not important ( since all selected members will get the same…

Q: Suppose there are 100 cans of green beans in a grocery store, and 75 of these are "Best Deal" brand…

A: There are 100 cans of green beans in grocery store. And 75 cans of these are "Best Deal" brand green…

Q: 5. From the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, if six-digit numbers are to be formed and…

A: 5) Total number of digits to be used 8 Unit digit can hold any of the 4-digits; 3,5,7,or 9 for an…

Q: Suppose, you have 3 different caps, 4 different shirts, 3 different pants and 3 pairs of socks and 2…

A: Depends on given data total outfits 3x4x3x3x2= 216  No need to wear socks and caps So total ways…

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

A:

Q: A committee of 5 is to be made from 3 students and 6 teachers. In how many ways can this be done a.…

A:

Q: 3. There are 5 doors in a Lecture Hall. In how many ways a student can enter the room through one…

A: Total number of doors in the lecture hall=5

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

A: There are totally 10 digits, the first digit has 9(Because first digit is nonzero) choices. Since…

Q: In how many ways can one black America and one Latino be selected from 15 black Americans and 6…

A: In order to get the result we have to calculate total no.of permutation.

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 carton of 15 light bulbs contains one that is defec-tive. In how many ways can an inspector choose…

A:

Q: A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated…

A:

Q: There are 6 roads from City A to City B, 8 roads from City B to City C and 9 roads from City A going…

A: Given : Number of roads from city A to city B = 6 Number of roads from city B to city C = 8 Number…

Q: A committee of 6 people is to be chosen from 5 men and 8 women. In how many ways can this be done (1…

A: Solution

Q: 8. There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and…

A:

Q: If 4 men and 5 women are having lunch together (a) in how many different ways can they order 2…

A: 4 men and 5 women 2 chicken, 4 turkey, 3 vegan

Q: Suppose that you must choose three people to meet with a customer. You have nine people to choose…

A: Given data, Total number of people (n)=9 Number of people to meet with a customer (r)=3

Q: Suppose that a department contains 10 men and 15 women. How many ways are there to select a…

A:

Q: how many ways to are there for eight men and ten women to stand in a line so that there would be…

A: Consider the given information. Number of ways to arrange tan women can be defined as, 10P10=10!…

Q: Six normal drinking glasses are standing in a row. The first three are full of water and the…

A: In this question we have to determine how can we change a one glass position so that no full glasses…

Q: A company has 7 male and 12 female employees, and needs to nominate 2 men and 2 women for the…

A:

Q: Of the 58 students in a mathematics​ class, 22 are taking​ French, 24 are taking​ German, and 7 are…

A: A Venn diagram is a pictorial representation of sets using circles or other closed figures inside a…

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.