A group of 12 people are going to run a race. The top 6 finishers are going to advance to the next qualifier. How many ways can the top 6 runners finish?

Q: At a NASCAR racing event, how many different finishes among the first 5 places are possible if 30…

A:

Q: How many license plates can we have of three digits followed by three letters? We allow repeated…

A: Since, there are 10 possible digits for the numbers (0 to 9), and 26 possible letters (A to Z). As,…

Q: A volleyball team will be dispatched from a school. If the current volleyball club has 10 members,…

A: A volleyball team has 6 members . Here, there are 10 members in club and we need only 6 of them.

Q: A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without​ looking, how many…

A: Given: There are total 4 oranges, thus it is not possible to get 5 oranges.

Q: Find the number of different ways that an instructor can choose 6 students from a class of 12…

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: In a​ company, 95​% of the workers are women. If 115 people work for the company who​ aren't women​,…

A: Let the total no.of workers are X. Given, 115 people aren't women . Then ,no of women workers=X-115

Q: Find the number of different ways that an instructor can choose 6 students from a class of 27…

A: Since he will choose a group of 6 students from a group of 27 students, so the arrangement does not…

Q: A group of 15 boys and 12 girls are planning to have a beach party. How many different committees of…

A: In how many different committees of 3 boys and 2 girls can be formed from this group of students if…

Q: A lottery has one $100 prize, two $25 prizes and five $10 prizes. What should you be willing to pay…

A:

Q: In a best-of-seven series in the Philippines Basketball Association (PBA) tournament, the team who…

A:

Q: There are 860 freshmen. If that is 43% of the class, how many are in the class?

A:

Q: The number of ways a team of 2 players can be chosen out of 12 players is

A: For the following question,

Q: If mark has 17 grapes And gives away 2. how Many does he have left?

A: Subtraction problem

Q: How many 3 card hands are possible with a 28​-card deck? The number of 3 card hands is ___

A: Total cards = 28

Q: The university of Montana ski team has 8 entrants in a men’s downhill ski event. The coach would…

A: Permutations: The number of permutations of r items selected from n items is, Prn=n!n-r! The…

Q: Find the number of different ways that an instructor can choose 4 students from a class of 26…

A: In this case, n = 26 and r = 4.

Q: Find the number of different ways that an instructor can choose 4 students from a class of 23…

A: Given: Number of students = 23 Number of students to be chosen = 4

Q: If there were only 9 Runners on the team last year how many females were there on the team this year

A:

Q: Find the number of different ways that an instructor can choose 6 students from a class of 26…

A: instructor can choose 6 students from a class of26 students.

Q: A casting director wishes to find one male and one female to cast in his plate if he plans to…

A: Given Male=9 Female=14

Q: Find the number of different ways that an instructor can choose 6 students from a class of 32…

A: choose 6 students from class of 32 students for a field trip. no. of ways to choose students = ?

Q: As a television executive, you have been given 24 shows to choose from to run during your prime time…

A:

Q: A teacher must pick 3 high school students from a class of 30 to prepare and serve food at the…

A: Suppose , we have n items. Then, the number of ways we can choose r number of items from n items…

Q: Find the number of different ways that an instructor can choose 6 students from a class of 29…

A:

Q: or a particular event, 697 tickets were sold for a total of $5250. If students paid $6 per ticket…

A:

Q: A softball league has twelve teams. If every team must play every other team once in the first round…

A: Topic: Permutations and combination

Q: You just got a free ticket for a boat ride, and you can bring along 3 friends! Unfortunately, you…

A: Given : Total number of friends = 5 Number of friends can bring = 3

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: A president, vice president, and 2 at-large members are selected for a school council from 10…

A: Combination:It represents the number of ways to choose x elements from a set of n elements. In…

Q: A mother duck lines her 12 ducklings up behind her. In how many ways can the ducklings line up?

A:

Q: Find the number of different ways that an instructor can choose 5 students from a class of 13…

A:

Q: the track team has 20 members and will be sending 5 members to the next competition. how many 5…

A: Given that, the track team has 20 members and will be sending 5 members to the next competition.

Q: A restaurant offers 8 entrees and 9 desserts. In how many ways can a person order a two-course meal?

A: We can find the answer as below.

Q: The organizer of a conference is selecting workshops to include. She will select from 7 workshops…

A: She has to select 6 workshops where atleast 5 must be about music. She can do it 2 way, i. she…

Q: If there are 5 logs in a pile of 30 that have sap on them, how many logs will have sap out of 360?

A: Given:--Number of logs that have sap on them in pile of 30 = 5 To Find:- Number of logs that have…

Q: A librarian noticed that 60% of seventh graders checked out fantasy books. About how many of 240…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4 were on time and 2 were late, how many of the next 12 trains would you expect to be on time?

A: The probability that the train would be on time is, Pon time=46=23 The probability that the train…

Q: If someone owns: 7 pants 1 shirt 5 ties 7 jackets, how many different outfits can that person make?

A: We have given that someone owns: 7 pants 1 shirt 5 ties 7 jackets

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

A:

Q: Find the number of different ways that an instructor can choose 4 students from a class of 18…

A: Combination:   It is nothing but the selection of objects where the order of selection is not…

Q: A business has 26 applicants for a job. How many ways can they pick 7 of the applicants to…

A: A business has 26 applicants for a job. To find how many ways can they pick 7 of the applicants to…

Q: As a television executive, you have been given 22 shows to choose from to run during your prime time…

A: Total number of shows Available n = 22 Total shows to be selected r = 12

Q: A different class has 275 ​students, and 56.4​% of them are men. How many men are in the​ class?

A: The total number of students in a class is 275 out of which 56.4 % are men.

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

A:

Q: Solve by the method of your choice: How many different ways can a director select 4 actors from a…

A: Given that : The number of actors in the group = 20

Q: Find the number of different ways that an instructor can choose 3 students from a class of 22…

A: From the provided information, There are 22 students from which 3 students will be chosen for a…

Q: A book club offers a choice of 5 novels from a list of 10. How many 5-novel selections can be made?

A: Given data: The total numbers of books are n=10. The numbers of novels selected are x=5.

Q: A girl has four skirts and six blouses. How many different skirt-blouse combinations can she wear?

A: The girl can wear 4 skirts in four patterns.While she can wear 6 blouses in 6 patterns.

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.