In how many different ways can the letters of the word KNOWLEDGE be arranged in such a way that the vowels always come together?

Q: There are 17 students in a class, and 5 of them will be chosen to go on a field trip. How many ways…

A: The objective of this question is to find out the number of ways in which 5 students can be chosen…

Q: Fifteen books are to be places in a shelf. The 15 books are composed of: 6 math books, 5 science…

A: Given information: No. of math books: 6No. of science books: 5No. of english books: 4Total no. of…

Q: 2./How many 9 letter words (not necessarily meaningful) can you make from the word CHEMISTRY if a./…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: You can answer any 19 questions from the 21 questions on an exam. In how many different ways can you…

A: Here it is given that the order is of no importance, we will use the combination rule here where we…

Q: There are 10 students in a class. In how many ways can an instructor give at most three students a…

A: n = 10 Let x represent the number of students given grade A.   The number of ways a student can be…

Q: In how many ways can an adviser assign a different task to 9 students from a class of 15?

A: Here we need to assign a different task then we would use combination.   Combination formula: C(n,r)…

Q: How many ways are there to select three diamond earrings from a box of ten diamond earrings,…

A: Total diamond earrings = 10 We have to select three diamond earrings from a box. Order does not…

Q: Suppose a business owner has a choice of 5 locations in which to establish her business. She decides…

A: A business owner has choice of 5 locations for establishing her business. Hence, we have to find the…

Q: 2./How many 9 letter words (not necessarily meaningful) can you make from the word CHEMISTRY if a./…

A: If there are n vacant inline spots and each spot can be filled by any of the m number of objects…

Q: From among the 36 teachers in a college, one principal, one vice-principal and the teacher-in-charge…

A: It is given that there are 36 teachers in a college. We have to appoint one principal, one…

Q: 1. When ordering a pizza from Alberto's, you were asked first to choose a type of crust: thin or dep…

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

Q: There are two copies each of 4 different books. In how many ways can they be arranged on a shelf?

A: GivenTwo copies each of 4 different booksTotal no.of books=2×4=8

Q: A mother, father, and their three children are to line up for a photo. In how many ways can these…

A:

Q: Q9. A search committee was formed to find a new software engineer from a set of 50 applicants. The…

A: From the given information, the number of candidates selected for an interview (n) is 8 and the…

Q: 7. Diane's Diner is running a special this month at the restaurant. You can order an appetizer, an…

A: Solution

Q: There are 10 students in a class. In how many ways can an instructor give at least one student a…

A: There are 10 students So sample size, n= 10 And we've to find ways for at least 1 student. So r= 1

Q: Suppose we want to choose 2 colors without replacement, from the 4 colors red,blue,green, and…

A: a.Find the number of ways in which 2 colours can be chosen among the 4 colours without giving…

Q: For each of the following, indicate if it is a problem involving permutations, combinations, or…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: Suppose you have 11 books and you randomly pick 4 to take on vacation with you. How many ways can…

A:

Q: 1. A student found 8 Mathematics books in the library. The library rules permit him to check out…

A:

Q: A committee of 6 people, with two of the six to be designated chair and vice-chair, is to be…

A: Number of ways of selecting 6 people of committee  from the group of 20 people will be:

Q: A artist donates 4 different paintings anf 5 different vases in a museum. The donations will be…

A: It is given that, there are 4 paintings and 5 vases.

Q: A computer user has downloaded 23 songs using an online file-sharing program and wants to create a…

A: GivenNo.of downloaded songs(n)=23no.of  songs to use in CD player(r)=8

Q: From a group of 20 nurses, 4 are to be selected to work a night shift. In how many ways can this be…

A:

Q: suppose that we wish to seat 10 people, 5 men and 5 women, in a row of ten chairs. in how many ways…

A:

Q: On Sunday mornings, I direct a church choir I am responsible for choosing the hymns. Suppose 20…

A: There are total 20 hymns. I have to pick 8 hymns. Given that the order does matter. So we can use…

Q: How many ways are there in choosing 3 books from a shelf of ( 83 ) books ?

A: The number of way for choosing 3 books from a shelf of 83 books is C383 =83!3!×(83-3)!…

Q: n how many different ways can we select a committee of a president, vice president , and a secretary…

A: Given,total no.of applicants=15

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.