There are 14 standbys who hope to get a seat on a flight, but only six seats are available on the plane.  How many different ways can the six people be selected and assigned to a specific seat?

Q: There are 12 people in a dinner gathering. In how many ways can they arrange themselves around a…

A: We use permutations and combinations. Number of ways to arrange n objects in n places is n! Number…

Q: There are 23 students in a class, and 6 of them will be chosen to go on a field trip. How many ways…

A:

Q: A clothing store has a selection of 80 different ties. How many ways can six ties be selected for…

A: It is given that, A clothing store has a selection of 80 different ties. Chris and Alex select 6…

Q: From a pool of 300 candidates the office of president, Vice President, secretary, and treasurer will…

A: Given that,Total number of candidates = 300Total number of required candidates = 4

Q: from a group of 21 people, how many different ways an a committee consisting of a president,…

A: Combinatorics are mathematical techniques that determines the number of possible arrangements in a…

Q: Find the number of ways in which we can select a team of 6 players from a class of 12 people.

A:

Q: in a qualifying race for a road cycling event, 15 men competed for five slots.How many different…

A: Given The total number of men (competed)=15 The number of slots=5 Apply permutation formula…

Q: From the 6 male and 11 female sales representatives for an insurance company, a team of 4 men and 2…

A:

Q: There are 18 males and 14 females in a classroom. A president, secretary and vice- president must be…

A: There are 18 males and 14 females in a classroom. A president, secretary and vice president must be…

Q: A New club at Arvin High has 22 members. In how many ways can the club elect a president and Vice…

A: The number of members in the club is 22. The number of ways of electing a president is C122=22.…

Q: There are 10 members on a board of directors. If they must elect a chairperson, a secretary, and a…

A:

Q: Out of the 12 people applying for a scholarship, a) how many ways can we select a group of five to…

A: N : number of students = 12 a) To select 5 people. = (12),(11),(10),(9),(8)  are the choices for…

Q: The supreme choice pizza at Pete's Pizza contains 3 different types of meat and 2 different…

A: It is given that a supreme choice pizza at Pete’s Pizza contains 3 different types of meat and 2…

Q: In a student organization, there are 11 freshmen, 8 sophomores, 19 juniors and 24 seniors. 1. How…

A:

Q: How many ways are there to choose 3 applicants from 8 job-seekers for high-paying positions in an…

A: Given information- We have given that in an engineering company 3 positions are there and 8…

Q: 4 freshmen and 2 sophomores from a sorority will attend a conference. If the sorority has 14…

A:

Q: If 15 people start a race, in how many different ways can the top 3 finishers be determined?

A: Permutation:   It  is an arrangement of objects in a definite order where the order is important.…

Q: There are 29 students in a homeroom. How many different ways can they be chosen to be elected…

A: Given,Total no.of students=29

Q: How many different committees of 3 people can be chosen from a group of 8 people?

A: Total number of people in the group are 8. Total number of people for the committee is 3.

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

A: Solution

Q: There are 12 members who are part of the student senate group. How many ways can the teacher…

A: We have to find the no of ways  can the teacher supervisor choose three of them to attend a…

Q: There are 11 goldfish in a fishpond. In how many ways can 5 be chosen to be moved to another…

A: →Whenever, we have to select r things without knowing order of selection    from n things , then…

Q: From the 11 male and 11 female sales representatives for an insurance company, a team of 4 men and…

A: From the 7 male and 6 female sales representatives for an insurance company, a team of 2 men and 2…

Q: From the 8 male and 9 female sales representatives for an insurance company, a team of 2 men and 3…

A: There are 8 men and 9 women representative for an insurance company, and we have to select 2 men and…

Q: A baseball team is having a walk-on tryout camp for players. Thirty-four players show up at camp,…

A: Number of players (n) = 34 Coaches choosing only (r) = 3 By using combination formula

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 the 12 male and 12 female sales representatives for an insurance company, a team of 4 men and 2…

A:

Q: There are 12 qualified applicants for 5 trainee positions in a department store. How many different…

A: Given There are 12 qualified applicants for 5 trainee positions in a department store. This problem…

Q: From the 9 male and 6 female sales representatives for an insurance​ company, a team of 4 men and 3…

A:

Q: The Cincinnati Angry Unicorns is a local swimming team which currently has seventeen members. If…

A:

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: 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: A company has 10 members on its boards of directors. In how many different ways can they elect a…

A: The total number of board of directors = 10. The officers need to be elected = 4 (President,…

Q: The newly elected president needs to decide the remaining 7 spots available in the cabinet he/she is…

A: The permutation formula is nPr = n!/(n-r)!

Q: From the 7 male and 6 female sales representatives for an insurance company, a team of 2 men and 2…

A: Given ,           No of males=7          No of females=6

Q: a restauranr offers 4 different flavors of coffee,3 different soup selections and 4 different…

A:

Q: There are 24 students in a math class. How many ways are there to select 3 students for a group…

A: There are 24 students in math class.  We have to find number of ways to select 3 students for group…

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: How many committees can be formed by choosing 4 men from an organization of a membership of 15 men?

A:

Q: The newly elected president needs to decide the remaining 5 spots available in the cabinet he/she is…

A: Given data; The number of spots available  in cabinet he/she is appointing(x) = 5 The eligible…

Q: How many ways can you select 3 students from a class of 30 students to serve as representatives for…

A: Follow the procedure given below.

Q: From a group of 7 men and 6 women, any five persons are to be selected to form a committee. In how…

A:

Q: There are 7 athletes at a track meet. How many different ways can they finish first, second, and…

A: Principle counting is a measure used for counting. It measure the number of possible outcomes in an…

Q: From a group of 20 people, 12 are selected to serve on a jury during a trial. How many different…

A: The total number of combinations possible if we select r things which are chosen at a time  from n…

Q: If 8 boats enter a​ race, how many possibilities are there for the first through third place​…

A: The numbers of different possibilities are obtained below: The permutation formula is shown below.…

Q: The president of the college asked a fraternity to submit a list of 7 students to serve as guides at…

A:

Q: There are 25 people in a club. In how many ways can the club elect a president, a secretary and a…

A:

Q: Your sister is shopping at an exclusive Rodeo Drive clothing store and examines 4 distinct blouses,…

A: It is given that there are 4 distinct blouses, 5 distinct dresses, and 2 distinct handbags. Since,…

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: Eight runners are hoping to take part in a race, but the track has only six lanes. In how many ways…

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.