After selecting nine players for a baseball game, the manager of the team arranges the batting order so that the pitcher bats last and the best hitter bats third. In how many different ways can the remainder of the batting order be arranged?

Q: At a furniture store, there a 4 different sizes of sofas, 7 different colors of fabric , and 8…

A: Given that, No.of  different sizes of sofas = 4 No.of different colors of fabric =7 No.of different…

Q: The eleven players of the CHS sepak takraw team are to be photographed for the team's tarpaulin. In…

A: Here, the question is in how many ways can 11 players can be arranged in a row.

Q: The coach of a volleyball team has to select 6 players to start a match from a squad of 10 players.…

A: The coach of a volleyball team has to select 6 players to start a match from a squad of 10 players.…

Q: A bride is choosing a dress for her bridesmaids. If there are 2 styles, 5 colors, and 3 fabrics, in…

A: Given that  A bride is choosing a dress for her bridesmaids. Number of styles = 2 Number of colors =…

Q: If 10 people are qualified for the next flight of a new space vehicle , how many different groups of…

A: Number of different ways to choose r number of people from a given set of n people is given by…

Q: A scholar is choosing six books to take on vacation from a stack of 34. A. How many different…

A: Solution

Q: A school principal plans to form teams from 132 third‐graders, 120 fourth‐graders, and 204…

A:

Q: How many different ways can 3 outfielders and 4 infielders be chosen from 9 outfielders and 7…

A: Given: How many different ways can 3 outfielders and 4 infielders be chosen from 9 outfielders and 7…

Q: A typist has 5 letters and 5 addressed envelopes. In how many different ways can the letters be…

A:

Q: A softball league has 13 teams. If every team must play every other team once in the first round of…

A: We are given that there are 13 teams and every team needs to play against every other team. For exam…

Q: Find the number of ways in which we can select a team of 6 players from a class of 12 people.

A:

Q: A photographer is asked to submit 7 photos from a collection of 14. How many ways can the photos be…

A:

Q: There are 12 people in a dinner gathering. In how many ways can they arrange themselves around a…

A:

Q: A softball league has eleven teams. If every team must play every other team once in the first round…

A:

Q: How many different ways can the golf pro at a golf club select a foursome consisting of 1 man and 3…

A: Given,   Number of males = 8 Number of females = 11   The objective is to find how many different…

Q: The table d'hote (complete meal) at a french restaurant consists of a salad, enree, and a dessert.…

A: There are 2 salad choices, 5 entrée choices, and 3 dessert choices.

Q: If 11 people are to be seated in a row of 11 chairs, how many different seating arrangements are…

A: Given: 11 people are to be seated in a row of 11 chairs. The objective is to find different seating…

Q: A developer of a new subdivision offers a prospective home buyer a choice of 4 designs, 3 different…

A: Let, N be the number of different available plansFirst operation (choice of home design) can be…

Q: If 15 people start a race, in how many different ways can the top 3 finishers be determined?

A: Permutation:   It  is an arrangement of objects in a definite order where the order is important.…

Q: How many different teams can be formed?

A: Given  there are 10 males and 8 females to find: needs to nominate 3 men and 3 women for the company…

Q: How many different committees of 3 people can be chosen from a group of 8 people?

A: Total number of people in the group are 8. Total number of people for the committee is 3.

Q: A bride is choosing a dress for her bridesmaids. If there are 3 styles, 4 colors, and 5 fabrics, in…

A: Given that, Number of styles = 3 Number of colors = 4 Number of fabrics = 5

Q: If 20 women are entered in the Miss Georgia contest, in how many different ways can the judges…

A: Given that 20 women are entered in the Miss Georgia contest.

Q: Ten jokes are listed in a magazine.   If the fourth joke from the magazine is​ excluded, in how…

A: There are 10 jokes listed in a magazine.Here 4th joke is excluded than find the number of ways…

Q: Renae, Nexael, Braden, Lovely, and Vanessa are attending a play and want to sit together in a row.…

A:

Q: How many different patchwork quilts, four patches long and three patches wide, can be made from five…

A: Given: Five red and seven blue squares.   To determine: The number of different patchwork quilts…

Q: A bag contains 15 pieces of candy. In how many ways can four pieces be selected?

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Q: In how many ways can you arrange 4 people to be seated in a round table?

A:

Q: How many different arrangements can be made using all the letters in CALGARY, if the first letter…

A: CALGARY If the first letter must be G.  Then, Starting with G, need to arrange the remaining 6…

Q: A softball league has twelve teams. If every team must play every other team once in the first round…

A: Topic: Permutations and combination

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

A: 2. There are 4 people Dylan,Andrew,Hailey and Jordan Here The places are also 4 The race are start…

Q: How many ways can a team of 28 hockey players choose a captain and two alternate captains?

A: Given that, There are 28 players in a hockey team.

Q: \item How many ways can a store manager arrange a group of 1 team leader and 3 team workers from his…

A: Note: As per our Honor code policy, we are authorized to answer only three sub parts at a time. So,…

Q: A teacher chooses 3 of her 22 students to help clean the room after school. In how many ways can the…

A:

Q: How many ways can you select 3 students from a class of 30 students to serve as representatives for…

A: Follow the procedure given below.

Q: A president, a treasurer, and a secretary are to be chosen from a committee with 30 members. In how…

A:

Q: How many different committees of three persons each can be chosen from a group of twelve people?

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

Q: If 8 boats enter a​ race, how many possibilities are there for the first through third place​…

A: The numbers of different possibilities are obtained below: The permutation formula is shown below.…

Q: A city soccer league has 8 teams.  In how many ways could the league assign first, second, and…

A: There are total 8 teams We have to pick 3 teams from those 8 teams.  Since it is ranking, so order…

Q: If 20 paintings are entered in an art exhibit, in how many different ways can the judges award a…

A: It is given that, 20 paintings are entered in an art exhibit. Then judge award the first prize to…

Q: From the 9 male and 6 female sales representatives for an insurance company, a team of 2 men and 2…

A:

Q: 6. If there are 12 teams in a basketball tournament and each team must play every other team in the…

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

Q: A contractor has three styles of homes, each with three styles of garages, two styles of decks, and…

A: Answer: First we need to list all the possible selections and the number of choices that each…

Q: A major league baseball team has 40 players of which 25 are considered active. a.) How many ways are…

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

Q: If you pick 4 cards without replacement from a standard deck of 52 cards, how many different…

A:

Q: Two freshmen and three sophomores from a sorority will attend a conference. If the sorority has 12…

A:

Q: rom the 7 male and 6 female sales representatives for an insurance​ company, a team of 4 men and 4…

A: It is given, Number of male representatives is 7, Number of female representatives is 6, A team of 8…

Q: 2. The view of Sampaloc Lake is a very nice background to take pictures of. How many ways can 5…

A: Find the number of ways of arrangement

Q: How many committees could be formed from 10 students if: a) there must be at least 8 people? b)…

A: Introduction: The number of different ways in which r different objects can be selected out of n…

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.