A group of nine people are attending the movies together.   (a) Two of the nine insist on sitting side-by-side. In how many ways can the nine be seated together in a row?   (b) Two of the people do not like each other and do not want to sit side-by-side. Now how many ways can the nine be seated together in a row?

Q: 3. They planned to make a chicken vegetable salad; thus, they bought carrots, potatoes, lettuce,…

A: The ingredients bought are: carrots, potatoes, lettuce, cabbage, pineapple quail eggs and chicken.…

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Q: In a bucket of tacos, we have 4 spicy beef tacos, 6 spicy chicken tacos, and 6 mild beef tacos. If…

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A: We have given that  Laura’s soccer team played a good season, finishing with 12 wins, four losses,…

Q: A group of 10 friends go out for dinner at a fancy dining room andthey each leave their hat with an…

A: A group of 10 friends go out for dinner. 5 of the friends were  wearing fedorasand and the other 5…

Q: n how many ways can 5 men, 4 women, and 3 children be arranged in a row of 12 seats if a. the men…

A: Given that  Number of men = 5 Number of women = 4 Number of children = 3 Number of seats in the row…

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Q: School is over, your family is planning a vacation somewhere outside the city, and your mom is…

A: Given,total no.of books=12no.of favorite books=5

Q: A teacher is decorating their classroom by placing posters in a row on one wall. The teacher has 7…

A: Explanation: a) Given that,  Choose 5 posters out of 7. P57=7!(7-5)!=7×6×5×4×3=2520

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A: Given, A college scholarship program awarded two more scholarships this year than last year. A total…

Q: Seven women and nine men are on the faculty in the mathematics department at a school. i.How many…

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

Q: Four married couples have bought 8 seats in the same row for a concert. In how many diff ways can…

A: Given: Four married couples have bought 8 seats in the same row for a concert.

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Q: A group of 12 people is traveling in three vehicles. If 4 people ride in each vehicle, in how many…

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Q: Rebecca has a collection of basketball cards. When she puts them in piles of two, she has one card…

A: Given: When she puts the basketball cards in piles of 2 there is one card left. Similarly when she…

Q: A tailor owner has 10 new pants that he wants to display in the window. If the display window has 4…

A: The number of new pants are 10.

Q: You were tasked to take charged of the auditions for the female part of the stage play. In how many…

A: Let us analyze this problem for a bit. A hopeful does not care if she is selected first, second or…

Q: you had a box of five different kinds of fruit and you could choose 2, you might get an apple and an…

A: Given that  Number of types of fruits (n) = 5 Number of fruits we could choose = 2   We know that…

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Q: A computer user has downloaded 25 songs using an online file-sharing program and wants to create a…

A: Here, we have to determine how many different permutations of 10 songs are possible from a set of 25…

Q: 100 people went to the amusement park.  51 went on roller-coasters, 29 went to the haunted house and…

A: Introduction: Suppose A, B, and C are three events, and n (A), n (B), and n (C) are the respective…

Q: A mail man has special -delivery for 10 customers. (i) In how many ways can he deliver to all? ii)…

A: i) deliver to all means arranging 10 customers in  all ways possible Total number of ways = 10! =…

Q: In a group of 15 students, 6 students are girls.  In how many ways can a team of 10  students be…

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Q: My grandson likes to play with cards (he always includes the jokers). First he drops the deck of…

A: Given information:Child always picks up at least 1 card, but he could pick up 1, all 54, or any…

Q: How many ways can a group of five boys and five girls be seated in a row of ten seats if boys and…

A: Here we have to find no. Of ways in the given problem.

Q: A Former gets 23.6 milk from each of his cows per day. He milks all four cows and pours the milk…

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Q: As a vacation souvenir, a family of 4 members wanted to be photographed together with their 2 pets…

A: A family of 4 members wanted to be photographed together with their 2 pets (a cat and a dog). Given,…

Q: A woman has 11 close friends. In how many ways can she invite 5 of them to dinner if two of them are…

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Q: 2. Oliveros family will eat at Mcdollibee Antipolo. In how many ways can Mr. Oliveros arrange his…

A: Given, 7 children and their parents sitting at a round dining table  To find the possible number of…

Q: 10. A shop sells 15 kinds of doughnuts, among them are plain, choco-filled, and strawberry-filled.…

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Q: A group of 10 friends go out for dinner at a fancy dining room and they each leave their hat with an…

A: Given: Total number of people is, N=10. Number of people wearing fedoras hat is, nf=5. Number of…

Q: 1. A school has 677 students. Explain why at least two students must have the same pair of initials?…

A: Note- As per our policy we can answer only 1st question. If you want solutions for other, then you…

Q: 4. Six people attend the theater together and sit in a row with exactly six seats. a. How many ways…

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Q: In a certain group of 50 students at Hogwarts School of Wizardry, only 15 students are wearing caps…

A: Let C be the group of students who are wearing caps and N be the group of students who are wearing…

Q: Chess clubs of two schools, School A and School B, consist of 5 and 20 players, respectively. If in…

A: Using the fact that n!=n·n-1···2·1. From the school A, 5 players can be chosen in 1 way. Number of…

Q: The top two students in the grade 12 mathematics' class are to receive awards for the highest mark…

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Q: t the Harris Burger Bar each customer designs their own burger by choosing: one from two types of…

A: Solution: Given information: The customers designs their own burger by choosing: one from two types…

Q: A high school tennis team is scheduled to play 28 matches. If the team wins 60% of the first 15…

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Q: 9 books in a row on his bookshelf. He will put one of the books, Hamlet, in the first spot. He will…

A: Given Data: Total books: n=9 First spot: One book, Hamlet Last spot:  One book Macbeth   In the…

Q: According to the authors of a certain​ book, in a global village of 200 ​people, 27 suffer from…

A: We can find the answer as below.

Q: a dinner gathering. In how many ways can the host (one of the 12) arrange his guest around a dining…

A: To find:  1.Number ways can the host arrange his guest around a dining table. 2.Number of ways three…

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Q: In a mathematics​ class, students received an A on the third​ test, which is ​% of the students who…

A: Step 1

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Q: Five Filipino, four Canadians, and four Brazilians are to sit at a circular table. In how many ways…

A: The permutation is used to calculated the number of arrangement in an ordered way, it is denoted as…