How many ways can a set of 10 different books be arranged on a shelf if they are not in alphabetical order? 9! 10! O9! 1 10! 1

Q: How many different numbers can be formed by various arrangements of the six digits 1, 1, 1, 1, 2, 3

A: Please refer to the solution in next step.

Q: In how many ways can 6 girls and 3 boys sit on a row of 9 chairs in such a way that no two boys sit…

A: we have to solve given problems:

Q: Find 1!, 2!, 4!, and 6!.

A: Factorial:

Q: How many ways can we choose 3 numbers from the set (1, 2, 3, 4, 5, 6, 7) (The order we choose…

A: Permutation:   It is nothing but the arrangement of items in a definite order where the order is…

Q: How many ways can 6 boys stand in a line if a certain boy must come first?

A:

Q: How many ways can 2 students be selected from a group of 5 students if order matters?

A: Solution-: We find number of ways 2 students be selected from a group of 5 students if order…

Q: Example 1 In how many ways can the word "BOOK" be arranged

A:

Q: How many numbers of four digits can be formed with the digits 0, 1, 2, 3 (repetition of digits being…

A:

Q: In how many different ways can a 4-child family have 2 boys and 2 girls?

A: To determine: Ways can a 4-child family have 2 boys and 2 girls.

Q: In how many ways can a team of 11 players be chosen from 14 players if the captain and his assistant…

A: This is problem of counting and we will solve this using combination.

Q: How many ways can three people be selected from a group of seven people if order DOES matter

A: Given that, Total number of peoples = 7

Q: How many ways exist to arrange 7 books (A, B, C, D, E, F, and G on the shelf,  if the books B and

A:

Q: 5 blue, 2 red, and 3 green books can be arranged how many ways if books of the same color are…

A: We have given that Number of blue books = 5  Number of red books = 2 Number of green books = 3

Q: How many ways can 4 books be arranged on a shelf if the books are selected from a collection of 100…

A: Here we will use the concept of permutation Permutation = nPr = n!/(n-r)!

Q: how many ways can Dr. Yes invite 8 of his friends if he has to invite at most 4 at a time?

A:

Q: There are 12 different books on a shelf. In how many ways can we take 4 of these books and put them…

A: Combination: A combination is a grouping or subset of items. for a combination, the order not…

Q: How many different ways can six different objects be arranged i

A: Factorial: n!=n*(n-1)*(n-2)*.....*2*1 Given that there are 6 different objects. That is, n=6

Q: A sports team has a record of 10 wins, 6 losses, and 1 tie. In how many ways can this record occur?…

A: The number of wins is 10.

Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, and 9, which are divisible by 5,…

A: Given information- We have given the digits- 2, 3, 5, 6, and 9. We have to form the 3 digits numbers…

Q: In how many ways can the numbers from 7 to 10 be arranged three at a time if the numbers can repeat?

A: If we have n numbers and we want to arrange k of them where the numbers can repeat, then the total…

Q: In how many ways can 7 people be seated in a row if only 4 chairs are available?

A: Here 4 chairs are available and 7 people can be seat.

Q: Six men and eight women are to line up for a picture with the six men in the middle. How many ways…

A: Given that  Six men and eight women are to line up for a picture with the six men in the middle  How…

Q: In how many ways can we seat 6 boys and 3 girls on a row of seats so that no two girls sit next to…

A: If no two girls can sit together, then we need to alternate boy and girl. We can start with a boy…

Q: In how many ways can you arranged 2 Math books, 3 Science books and 3 English books if only one book…

A: The total number of mathematics books are 2. The total number of science books are 3. The total…

Q: How many different 10-letter words (real or imaginary) can be formed from the following letters? G,…

A: There are 10 letters; G, P, W, R, K, V, P, A, F, P

Q: Bob owns 13 different books. He wants to pick out and arrange 5 of these books left-to-right on a…

A:

Q: How many ways can these numbers be arranged? How many numbers greater than 4,000,000 can be formed…

A: Here use combination

Q: How many elements are in the set {2,2,2,2}

A: We have to find number of elements

Q: How many 4 digit numbers can be formed using only the numbers 3 2 7 6 0 4 9 if the number is odd and…

A: numbers: {3,2,7,6,0,4,9} make 4 digit numbers  no repeatation odd numbers: last digit must be odd.…

Q: In how many different ways can five red flags, two white flags, and 7 blue flags be arranged in a…

A: If all the flags were distinct, each flag being a different color, there would be 14! different…

Q: How many different 5-digit odd numbers can be formed from 0, 1, 3, 4, 5, 7, and 9 if repetitions are…

A: Given:Total number of digits = 7 (0, 1, 3, 4, 5, 7, and 9 ) The divisibility rule for 5:The number…

Q: How many 4 letter words can be created using the letters in the word COMPLICATED?

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: how many ways can a teacher sit 12 students in two rows of 6 chairs if Bobby must sit in the front…

A: Given: Total number of students = 12 Number of seats in each row = 6 Bobby is in first row and Billy…