Suppose you are asked to list, in order, the three best movies you have seen this year. If you saw 12 movies during the year, in how many ways can the three best be chosen and ranked?

Q: How many choices are there for a person to check out 4 CDs from a library that has 25 CDs of his…

A: Given : n = 25 x = 4

Q: How many ways can you choose first, second, and third place winners from 15 people?

A: The first place winner can be chosen as 15 ways. The second place winner can be chosen as 14 ways…

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

A:

Q: You must select 3 individuals from a group of 5 for a conference. How many teams of 3 might you…

A:

Q: How many ordered lists are there of three items chosen from four? ?ordered lists

A: According to the problem, we have

Q: In a lottery game, a player picks 9 numbers from 1 to 49. How many different choices does the player…

A: From the provided information, A player picks 9 number from 1 to 49. Total number = 49

Q: If a person can select five books from a list of ten, how many different combinations are there?

A: Given data: The total numbers of books are n=10. The number of books selected is r=5. The expression…

Q: Assume that 15 exhibits entered the science fair, and that we want to assign 3 prizes: first,…

A:

Q: In a lottery game, a player picks 9 numbers from 1 to 49. How many different choices does the player…

A: In a lottery game, a player picks 9 numbers from 1 to 49. That is, the total numbers is 49 and…

Q: How many ordered lists are there of three items chosen from ten? ? ordered lists

A:

Q: How many ordered lists are there of eleven items chosen from fourteen?

A: Ordered lists are the lists in which position of each one matters  This can be solved by using…

Q: In a race of 24 people, the top 8 are awarded different amounts of prize money, with first receiving…

A: Permutation: The number of different arrangements of ‘r’ elements (order matters) from a set of ‘n’…

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: 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: How many ordered lists are there of seven items chosen from twelve?

A:

Q: in a survey of 80 fifth grade students who play soccer,basketball,or both,60 students play and 40…

A: Form the given information, In a survey of 80 fifth grade students who play soccer, basketball or…

Q: How many ordered lists are there of two items chosen from twelve?

A:

Q: How many ways are there to choose first, second, and third prizes in an art contest with 18 entries?

A: Introduction:According to the permutation rule, if r distinct items are to be chosen from n items…

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

A: Solution

Q: If you can choose one item from a group of M items and a second item from a group of N items, then…

A: we have chose 1 item from a group of M items  and second item from a group of N items

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: From a group of 36 people, a jury of 12 is selected. In how many different ways can a jury of 12…

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

Q: Ten jokes are listed in a magazine.   If the fourth joke from the magazine is​ excluded, in how…

A: There are 10 jokes listed in a magazine.Here 4th joke is excluded than find the number of ways…

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

A:

Q: In a survey of 1000 students it was found that 840 own a cell phone, 450 own an MP3 player and 370…

A:

Q: How many ordered lists are there of seven items chosen from eight? ordered lists

A: Given n=8 r=7

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

A:

Q: Consider a group of N people. If everyone shakes hands with everyone else, how many handshakes take…

A: The number of people in a group is N.

Q: In a class of 18 girls and 15 boys, in how many ways can a girl get the highest grade, a boy second,…

A: Consider the given information.The number of the boys is 15 and the number of the girls is 18 girls.

Q: how many ordered lists are there of three items chosen from six ?

A:

Q: A woman has two skirts and six blouses. Assuming that they all match, how many different skirt and…

A: As we know, nCx=n!(x)!  *  (n-x)! ; where n!=1*2*3*.....(n-1)*n

Q: How many ordered lists are there of two items chosen from five?

A: To find the number of ordered lists.

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: The “Top Three” at a racetrack consists of picking the correct order of the first three horses in a…

A:

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: How many ordered lists are there of five items chosen from ten

A: According to the given information in this question We need to find the value of P(10,5) We know…

Q: A company conducted a marketing survey of its clientele and found that 215 own an iPhone and 106 own…

A: It is given that 215 of the clients own an iPhone and 106 own an iPad. If 19 clients own both an…

Q: A photographer is asked to submit seven photographs from a collection of 14 for an exhibit. In how…

A:

Q: How many ways can you choose 5 out of 10 friends to invite to a dinner party?

A: To solve the problem of combinations (selections) in the given scenario.

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: What are all the ways in which the top 4 racers in a 20 person race can finish?

A: Introduction:In the given situation, the number of persons participated in the race is 20. The…

Q: If 20 paintings are entered in an art exhibit, in how many different ways can the judges award a…

A: It is given that, 20 paintings are entered in an art exhibit. Then judge award the first prize to…

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: A company conducted a marketing survey of college students and found that 191 own a bicycle and 74…

A:

Q: Suppose you are asked to choose three movies. If there are 20 different movies, in how many ways can…

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

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: How many ordered lists are there of two items chosen from six?

A:

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

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:

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.