Suppose that a certain football tournament consists of 16 teams: 6 from Europe, 3 from South America, 3 from Africa, 2 from North America and 2 from Asia. Four teams will make the finals. For each of the following, show working to justify your answer. Evaluate all answers as numbers (i.e. do not leave them in terms of combination notation, or factorials). How many different possible combinations of finalists are there if (a) there are no restrictions? (b) exactly one South American team is in the finals? (c) no team from North America makes the finals? (d) at least two non-European teams make the finals? (e) The four finalists are from different regions?

Q: In a “Pick-4” game, a player wins a prize for matching a 4-digit number from 0000 to 9999 with the…

A: Given: A player wins a prize for matching a 4-digit number from 0000 to 9999 with the number…

Q: Suppose we want to choose 5 letters, without replacement, from 15 distinct letters. (a) How many…

A: Solution-: Here, n=15,r=5 We want to choose 5 letter, without replacement from 15 distinct letter.…

Q: At the DVD rental store, Jamie found 6 DVDs that she wanted, but can only rent 4. How many possible…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: In an adult literacy program, 2 teaching methods are being considered. To compare their relative…

A: The hypothesis test is a statistical method in which one using the sample data try to check the…

Q: 2 students is to be chosen from a 32-member class to represent the class on the student council. How…

A: Permutation: The procedures of permutation and combination are used to count the number of…

Q: Fifty (50) students in a school played Basketball and Football. Every student plays at least one of…

A:

Q: At a movie​ festival, a team of judges is to pick the​ first, second, and third place winners from…

A: It is given that there are totally 19 films entered at a movie festival.

Q: A volleyball team has ten players. To play a game, 6 players are needed to play positions numbered…

A: No. of players in the volleyball teamNo. of players needed to playThe positions are numbered from…

Q: Cookies (4 Circle-shaped, 8 Heart-shaped, 3 Bear-shaped) Suppose you draw one cookie from the box at…

A: It is given as18 Chocolate Cookies (8 Circle-shaped, 6 Heart-shaped, 4 Bear-shaped) 15 Vanilla…

Q: A team composed of two grade 11 and two grade 10 students is to be sent to a debate contest. If…

A: The provided information is  There are Two grade 11 and two grade 10 students  There are also 60…

Q: Among nine presidential candidates at a debate, three are Republicans and six are Democrats. In how…

A: Answer :- A) the nine candidates can be lined in =9! Ways  B) Answer :- I take  DDDDDDRRR  is 9C6…

Q: Suppose that a class of 20 students is assigned to write an essay.       Suppose 3 essays are…

A: Total number of students = 20 Total number of groups of selecting 3 essays can be obtained as:

Q: As the project manager of a project, you are in charge of a team of seven people which includes…

A:

Q: Which of the following notations could be used to determine the total number of possible ways in…

A: We have given that total of 500 attendees from which 15 were elected as Board of Directors. Three of…

Q: 1. Find the value of k that makes f(x) a valid pdf. -{ f(x) = k(3+x), 0≤x≤2 elsewhere 0,

A: From the information, given the pdf is,

Q: How many different Kriyas may be created with only 5 of these poses?

A: In yoga, a Kriya is a complete set of specific poses and breathing techniques that are combined to…

Q: There is a factory that makes widgets in different colors. The production time for each color is…

A:

Q: An engineer is putting together a train with 5 box cars, 3 tank cars, and 4 flat cars. For the box…

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

Q: Suppose that there are 9 female and 12 male students in a classroom. How many different 5-member…

A: Combination:   A combination is a selection of objects where order is not important.   If n is…

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: Find the number of permutations using 4 different letters a, b, c, and d, if they are taken 2 at a…

A:

Q: 10 people are in a club. How many ways are there to form a committee consisting of members of the…

A: 1. Number of ways to form a committee consisting of members of the club such that the committee has…

Q: Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate…

A: Given 16 smokers 22 non smokers

Q: Decide whether you would use a permutation, a combination, or neither. Next, write the solution…

A:

Q: A computer programming team has twelve members. Suppose five team members are women and seven are…

A: We find the number of groups of five that can be chosen with three women and two men from a team of…

Q: A committee of 4 people is to be chosen from a group of 8 men and 7 women. How many different…

A:

Q: A team of 6 people is to be chosen from a group of 7 girls and 4 boys. There ae possible teams if…

A: Combination formula :  Number of ways to select  r items from total n items is given by,   Crn =…

Q: Suppose that your friend owns 9 PlayStation games and you would like to borrow 4 of these games. In…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: For the rest of the problems in this section, decide whether to use permutations or combinations.…

A: Given: Number of yellow marbles=3 Number of white marbles=4 Number of blue marbles=9 Total number of…

Q: 2. Molly really enjoyed country music. After listening one afternoon to her favorite station foran…

A: The given information:There are a total of 25 songs. All the truck drivers are in love. Three fourth…

Q: . How many different ways are there of handing out the prizes if (a) the prizes are all the same?…

A: A kindergarten class has 18 children. FIve of the children are selected to receive prizes. Here use…

Q: From a class containing 5 boys and 6 girls a group of 5 students is to be selected. There are how…

A: We have given that Number of boys = 5 Number of Girls = 6 We have to select 5  students

Q: A large research project is looking for more researchers. There are 8 spots open on the research…

A:

Q: black hair or had a whole row to themselves (or both). Of this total, 25 had black hair and 5 were…

A:

Q: Los Angeles Dodgers. From the official website of the 2013 Los Angeles Dodgers major league baseball…

A: Given info:Five active players available on roster to play outfield.

Q: There are 16 teams in each conference in professional football, and 6 make the playoffs each year.…

A: The number of teams (n) is 16 and the number of playoffs for each year (r) is 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.