As a television executive, you have been given 22 shows to choose from to run during your prime time slots each week. If you have to choose 12 shows to run on your network, how many ways can you choose which shows to pick up?

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: When ordering a certain type of computer, there are three choices of hard drive, four choices for…

A: when ordering a certain type of computer, there are 3 choices of hard drive, 4 choices for the…

Q: A couple has narrowed down the choices of a name for their new baby to 4 first names and 6 middle…

A:

Q: A bride is choosing a dress for her bridesmaids. If there are 2 styles, 5 colors, and 3 fabrics, in…

A: Given that  A bride is choosing a dress for her bridesmaids. Number of styles = 2 Number of colors =…

Q: How many ways are there to pick three dipping sauces, if you can pick three of the same?

A:

Q: In a certain pizzeria you can choose among 3 sizes, 2 crust options, and 5 toppings. If it is…

A:

Q: in a physiology class, a student must dissect three different specimens. The student can select one…

A: This question can be solved using the concept of combination.

Q: in a volleyball club there are 5 senior players and 5 junior players. If the team captain election…

A: Total number of players = 10 Total number of players in volleyball team = 6   Number of ways in…

Q: A book club offers a choice of 2 books from a list of 20.  In how many ways can a member make a…

A: Since the order of the books matters so we will use the permutation method here.  There are total 20…

Q: In a club of 15 people, we need to choose a president, vice-president, secretary, and treasurer. In…

A:

Q: The table d'hote (complete meal) at a french restaurant consists of a salad, enree, and a dessert.…

A: There are 2 salad choices, 5 entrée choices, and 3 dessert choices.

Q: There are 6 men and 8 women auditioning to be in the school play. Answer the following questions: 1.…

A: Given that there are 8 women and 6 men

Q: The math club needs to select a President, Vice President, Treasurer and Secretary from their 20…

A:

Q: There are 6 women and 9 men signed up to join a swing dance class. In how many ways can the…

A: Given Information: There are 6 women and 9 men signed up to join a swing dance class. We are asked…

Q: On Halloween, a cartoon character, a bumble bee, a viking, a forest ranger, and a butterfly ring the…

A: here 6 people are in line and come one by one.  here order os selection matters  so this is case of…

Q: Before the election, you want to determine the number of possible president/vice-president…

A: Solution

Q: on the 12 chefs hat you own, you only have room to pick 5, how many different collections of chefs…

A: Given  Total chefs hat = 12 To pick number of room = 5 To find different collections of chefs hat…

Q: A bride is choosing a dress for her bridesmaids. If there are 3 styles, 4 colors, and 5 fabrics, in…

A: Given that, Number of styles = 3 Number of colors = 4 Number of fabrics = 5

Q: From a group of 20 children, how many must you choose, if you want to make sure two of them have…

A: There are 12 month in a year, thus let m=12. Let n denote the number of chosen children who have…

Q: Suppose you are asked to list, in order, the three best movies you have seen this year. If you saw…

A: Suppose you are asked to list, in order of preference, the three best movies you have seen this…

Q: From a group of 12 student representatives, 5 will be chosen to work on a committee. How many…

A: From a group of 12 student representatives, 5 will be chosen to  work on a committee. To determine…

Q: If there are 10 multiple-choice questions on an exam, each having three possible answers, how many…

A: From the provided information, There are 10 multiple-choice questions on an exam. Each question has…

Q: A college golf team consists of four players who are ranked from 1 through 4. If a golf coach has…

A: Given that a college golf team consists of four players who are ranked from 1 through 4.

Q: A bride is choosing a dress for her bridesmaids. If there are 3 styles, 5 colors, and 4 fabrics, in…

A: Given: Styles = 3 Colors = 5 Fabrics = 4 The number of ways that she can select the bridesmaids…

Q: If a club consists of 13 members, how many different arrangements of president, vice-president, and…

A: Here we have to arrange president, vice president and a secretary. An office can be run by only one…

Q: The All-County Goat Show will award the blue ribbon for 1st place, red ribbon for 2nd place, and…

A: Using permutations and combination

Q: If a club consists of 18 members, how many different arrangements of president, vice- president, and…

A:

Q: 2. Your friend Carlos brought over 10 videos. Together, you choose 4 of them to watch. How many…

A:

Q: There are 5 men and 7 women auditioning to be in the school play. Answer the following questions: 1.…

A: Given that : There are 5 men and  7 women auditioning to be in the school play.  Total cast  = 5+7 =…

Q: The library is to be given 3 books as a gift. The books will be selected from a list of 17 titles.…

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

Q: How many ways can a team of 28 hockey players choose a captain and two alternate captains?

A: Given that, There are 28 players in a hockey team.

Q: A boy owns 3 pairs of pants, 1 shirts, 7 ties, and 5 jackets. How many different out he must wear…

A: From the provided information, A boy owns 3 pair of pants, 1 shirt, 7 ties and 5 jackets.

Q: In a local club composed of 27 people, how many ways can 1 president, 1 vice President, 1 secretary…

A: Total number of people composed = 27

Q: Suppose you have a choice of ten TV sets that can be matched with any of six DVR players and eight…

A: Multiplication rule of counting: If a task consists of a sequence of choices in which there are ‘a’…

Q: There are 4 men and 7 women auditioning to be in the school play. Answer the following questions:…

A: The number of ways 2 women , and 2 man can be selected from 4 men and 7 women is,…

Q: A class of 40 students is to choose a set of classroom officers composed of the President,…

A: Permutation formula : nPr = n! /(n-r)!

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: There are five action, three drama, and four comedy films showing at a local  mall. If Phoebe goes…

A:

Q: If a club consists of 12 members, how many different arrangements of president, vice-president, and…

A: Given that  a club consists of 12 members. We have to find the number of different arrangements of…

Q: A restaurant offers a choice of 5 salads, 15 main courses, and 9 desserts. How many possible…

A: We have find the probability of given problem.

Q: As a television executive, you have been given 19 shows to choose from to run during your prime time…

A:

Q: 14 people try out for a basketball team, how many different ways are there to select 5 players if…

A: Given information: Total number of people who try out for a basketball team(n)=14. Number of…

Q: There are six men and seven women in a ballroom dancing class. If four men and four women are chosen…

A: Given:  Total No of Men=6 Total No of Women=7 Formula used: The formula for combinations is given…

Q: There are 5 men and 8 women auditioning to be in the school play. Answer the following questions: 1.…

A: Given : Number of men = 5 Number of women = 8

Q: A restaurant offers a choice of 4 salads, 13 main courses, and 6 desserts. How many possible…

A: Permutation and Combination: The different methods in which objects from a set could well be…

Q: If you pick 4 cards without replacement from a standard deck of 52 cards, how many different…

A:

Q: In a company, you need to pick from your employees to be the manager, the supervisor, the…

A:

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 seven boys and five girls in the debate squad at Franklin High School. In how many ways…

A: Given: Number of boys = 7 Number of girls = 5 Number of members selected = 4 Number of boys required…

Q: As a television executive, you have been given 8 shows to choose from to run during your prime time…

A: Total number of shows available = 8 Available time slot = 6

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.