An algebra class has 12 students and 12 desks. For the sake of variety, students chang thhe seating arrangement each day. How many days must pass before the class must repeat a seating arrangement? Suppose the desks are arranged in rows of 3. How many seating arrangements are there that put Larry, Moe, & Curly in the front seats?

Q: During the fall semester a school is offering science courses in physics, biology, and chemistry,…

A: It is given that there are science courses in physics, biology, and chemistry, and humanities…

Q: A group of five boys (Alex, Bryan, Chris, David, and Ethan) and three girls (Megan, Nancy, and…

A:

Q: In how many ways can you seat 2 children and 5 adults in a row if the children must be seated at…

A: Given: In how many ways can you seat 2 children and 5 adults in a row if the children must be seated…

Q: How many ways can 3 female students and 4 male students be seated on a long bench if the bench can…

A: To accommodate 3 female students and 4 male students, there are so many possibilities like all the…

Q: A theater has 29 rows of seats. The first row has 22 seats, the second row has 26 seats, he third…

A:

Q: f. In Carinderia Tomasino, a combo meal consists of a cup of rice, a bowl of soup, a serving of…

A:

Q: A boy owns 6 pairs of pants, 9 shirts, 10 ties, and 4 jackets. (a) How many outfits can he wear to…

A: Given data:     The given pairs of pants are: P=6. The given number s of shirts are: S=9. The given…

Q: In a classroom of 49, if 2. of the students are in the band and play sports, how many students do…

A:

Q: In a class there are 30 female students and 20 male students. A committee of four students need to…

A: There are 30 female and 20 male students.

Q: Investigative Team The state narcotics bureau must form a 5-member investigative team. If it has 30…

A:

Q: The director of the school play has to assign 5 lead roles. If the roles are being chosen from a…

A:

Q: How many ways can the letters of the word MAILBOX be arranged in a row if M and A must remain…

A: We can use permutations to find the solution to this problem. The number of permutations in a set of…

Q: A senate committee has 15 members.  If a subcommittee of 6 senators is to be formed from the…

A:

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

Q: A committee of 5 students is to be chosen from 6 boys and 5 girls 2. How many committees will…

A: Given,no.of boys=6no.of girls=5total no.of students=11

Q: At a corporate dinner, five people including the president and vice president are sitting around a…

A: a) If 5 people sit on a circular table then the number of permutations will be 4!=24 b) If President…

Q: An ice cream store sells 2 ​drinks, in 3 ​sizes, and 7flavors. In how many ways can a customer…

A: Given, An ice cream store sells 2 ​drinks, in 3 ​sizes, and 7 flavors.  We have to find , in how…

Q: A president, vice president, and 3 at-large members are selected for a school council from 9 people.…

A: Given that president, vice president and 3 at-large members are selected from 9 people.   Number of…

Q: At a dinner party, 6 men and 6 women sit in a round table. In how many ways can they sit if Bob,…

A: Number of ways to arrange N person around the round table is (N-1)!. Here, there are 6 men and 6…

Q: A sixth grade class is having a pizza party. The teacher ordered 5 cheese pizzas, 5 pepperoni and 5…

A: Fractions are used to symbolize a part of a whole.

Q: 2. Dylan, Andrew, Hailey, and Jordan ran in a race of 25 people. In how many different orders can…

A:

Q: At a deli counter there are 7 sandwiches with meat and 6 vegetarian sandwiches. Carols is at the…

A:

Q: n soccer, a tie at the end of regulation time leads to a shootout by three members from each team.…

A: Given that  Number of players available (n) = 11 Players need to be selected = 3   We know that We…

Q: A boy owns 10 pairs of pants, 6 shirts, 2 ties, and 9 jackets. (a) How many outfits can he wear to…

A: Multiplication rule of counting: If a task consists of a sequence of choices in which there are ‘a’…

Q: How many different ways can a visiting nurse visit  9  patients if she wants to visit them all in…

A: number of patients n=9   Different number of ways that n different items can be arranged is n!…

Q: A school dance committee is made up of 4 freshman, 4 sophomores, 3 juniors, and 2 seniors. How many…

A: Given 4 freshman 4 sophomares3 juniors 2 seniorsstudents must fit together by gradeF1F2F3F4…

Q: A grocery store has 6 checkout counters and 7 clerks. How many different ways can the 7 clerks be…

A: We have to find number of ways 7 clerks be assigned to 6 counters.

Q: A basketball fan has a pair of tickets to 6 different home GAMes of the Los Angeles Lakers. If the…

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

Q: To fill a number of vacancies, the personnel manager of a company has to choose three secretaries…

A: The number of ways a company has to choose three secretaries from among ten applicants can be done…

Q: a chief can prepare 20 different dinners. in how many ways can he select 6 of them for todays menu

A:

Q: A party room has a circular table with 12 seats. A group of 4 people enter the room. How many…

A: In a circular table with n seats,  there are (n-1)! ways ofoccupying the seats

Q: Jodi delivers 54 newspapers on Saturday and 78 newspapers on Sunday she makes bundles of 6…

A: Given: Jodi delivery newspaper on Saturday =54 Jodi delivery newspaper on Sunday =78 She makes…

Q: A teacher bought 20 apples. She wants to distribute the apples to 5 children. However, she decides…

A: As the student wants the answer of 1 (b), so, I will provide the answer to that part only.

Q: A school dance committee is made up of 2 freshman, 5 sophomores, 2 juniors, and 5 seniors. How many…

A: Given Data- A school dance committee is made up of: Freshman =2 Sophomores = 5 Juniors = 2 Seniors =…

Q: In how many ways can you choose 3 kinds of ice cream and 2 toppings from a dessert buffet with 10…

A: Given that there are 10 kinds of ice cream and  6 kinds of toppings. We can choose 3 kinds of ice…

Q: A disc jockey (DJ) has 7 songs to play. Four are slow songs, and 3 are fast songs. Each song is to…

A:

Q: An ice cream parlor has 28 different flavors, 8 different kinds of sauce, and 12 toppings. a. In how…

A: Given that, An ice cream parlor has 28 different flavors, 8 different kinds of sauce, and12…

Q: Three hungry pirates, Ahab, Bluebeard, and Hook, were stranded on a desert island. They came upon a…

A: Here we solve the problem by algebra.

Q: How many ways are there to sit the committee in a row at a meeting if the students must sit together…

A: This is question from permutation and combination

Q: Mr Regpala needs the help of 6 students from the class to help him move some supplies. If the class…

A: Given that  Mr Regpala needs the help of 6 students from the class to help him move some supplies…

Q: A teacher bought 20 apples. She wants to distribute the apples to 5 children. However, she decides…

A:

Q: 3. Marty is a bookworm and he has various collections of novels, series and other story books. If he…

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

Q: A bride is choosing a dress for her bridesmaids. If there are 5 styles, 2 colors, and 7 fabrics, in…

A: There are 5 styles, 2 colors, and 7 fabrics.

Q: A class of 15 students needs to elect a class president, vice president, treasurer, and secretary.…

A: Consider the given information. The class have 15 student and there are four position as given in…

Q: (i) How many ways are there to seat five different boys and five different girls along one side of a…

A: (i)

Q: A bakery sells 6 different kinds of pastry (and has at least 12 of each kind). (A.1) How many…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: A donut shop has 5 varieties of donuts and we want to order 10 donuts. But today, among their 5…

A:

Q: A disc jockey (DJ) has 11 songs to play. Five are slow songs, and 6 are fast songs. Each song is to…

A:

Q: eam. If you had a choice of having a single flavor of ice cream in a cone, a cup, or a sundae, how…

A: apply combination

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.