A motorcycle shop has 78 choppers, 72 bobbers, and 49 café racers—different types of vintage motorcycles. How many ways can the shop choose 1 chopper, 1 bobber, and 1 café racer for a weekend showcase?

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

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Q: A casting director wishes to find one male and one female to cast in his play. If he plans to…

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Q: There's a club of 10 men and 13 women. In how many ways can they choose a president, Vice President,…

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Q: In a club with 20 members, how many ways can a slate of 3 officers consisting of president,…

A: This question is related to permutation and combination. The solution is given below

Q: A basketball team consist of two centers, five forwards and four guards. In how many ways can the…

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Q: In the United States Senate, each state is represented by one junior senator and one senior senator.…

A: From the given information. The total number of states in the Midwest is 12. Each state is…

Q: A restaurant offers 4 different flavours of coffee, 3 different soup selections and 4 different…

A: From the provided information, A restaurant offers 4 different flavours of coffee, 3 different soup…

Q: You have 3 science books, 2 language books, and 4 philosophy books. In how many ways can they be…

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Q: A jury pool consists of 27 people. How many different ways can 11 people be chosen to serve on a…

A: 1. From the given information, a jury pool consists of 27 people.

Q: A club has 21 sophomores and 13 freshmen president, secretary, and a committee of four, what is…

A: so it can be solve by using

Q: A class consists of 60 girls and 40 boys. In how many ways can a president, vice-president,…

A: Number of boys=40 Number of girls=60 Given the treasurer must be a girl. Hence the number of ways to…

Q: A company has 42 employees. How many different ways can 7 people be chosen to serve on a committee…

A: We can choose the 7 persons in 42C7 ways  Where 7 people are chosen then there are (42-7)=35 people…

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

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Q: A man owns 8 pairs of pants, 15 shirts, 12 ties, and 3 jackets. How many different outfits can he…

A: Given he has 8 pairs of pants, 15 shirts, 12 ties, and 3 jackets

Q: A company has 10 male and 11 female employees, and needs to nominate 2 men and 2 women for the…

A: They can choose 2 men from 10 men in 10C2 ways They can choose 2 women from 11 women in 11C2 ways.…

Q: There are 7 highway routes from City A to City B, 9 highway routes from City B to City C, and 5…

A: Concept :  Fundamental principal of counting : If there is m ways to do one thing, n ways to do…

Q: At a local restaurant, a dinner special consists of choosing a salad, an entree and a dessert. If…

A: If there are 3 choices for salad, 6 choices for the entree, and 4 choices for dessert. At a local…

Q: How many ways can a delegation of 5 Republicans, 5 Democrats, and 2 Independents be selected from a…

A: As we need to choose any 5 republicans from a group of 7 republicans, so we have 7C5 possible ways.

Q: n a warehouse, there are several boxes of mixed screws. you pick up one with 100 screws in it. if…

A: Given: n (S) = 46 N (L) = 100 - 46          = 54 n (L ∪ F) = 74 n (L ∩ C) = 30 n (Total) = 100 S =…

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: In the United States Senate, each state is represented by one junior senator and one senior senator.…

A: It was stated that United States Senate, each state is represented by one junior senator and one…

Q: A catering service offers 5 appetizers, 4 main courses, and 6 desserts. A customer is to select 4…

A: Given: Number of appetizers=5Number of main courses=4Number of desserts=6 It is also provided that,…

Q: A boy owns 7 pairs of pants, 2 shirts, 20 ties, and 7 jackets.  How many different outfits can he…

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Q: A president, vice president, and 2 at-large members are selected for a school council from 7 people.…

A: It is given that 4 persons (a president, vice president, 2 at-large members) are selected for a…

Q: A student has 4 different biology books, 4 different chemistry books, and 5 different physics books.…

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Q: A man owns 6 pairs of pants, 7 shirts, 8 ties, and 2 jackets. How many different outfits can he wear…

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Q: there are 651 6th grade students at a school, and three out of every seven of them play a sport, how…

A: Given   Number of 6th grade students : 651   If 3/7 plays sports,    Then who don't play a sports…

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: The 50 members of a club include both the club president and the club treasurer. All 50 members want…

A: Topic- permutations and  combinations

Q: The board of directors of a corporation must select a president, a secretary, and a treasurer. In…

A: Given that there are total 14 members.    A president, a secretary, and a treasurer represent 3…

Q: A catering service offers 4 appetizers, 11 main courses, and 9 desserts. A customer is to select 2…

A: It is given that Number of appetizers = 4 Number of main courses = 11 Number of desserts = 9

Q: If a club consist of 15 members, how many different ways are there for the club to fill the…

A: The number of members is 15. The number of position is 3.

Q: There are 7 women and 6 men signed up to join a ballroom dance class. In how many ways can the…

A: Given: Number of men = 6 Number of women = 7 Number of people to join dance class = 4

Q: In how many ways can a subcommittee of eight be chosen from a Senate committee of seven Democrats…

A: We have to find In how many ways can a subcommittee of eight be chosen from a Senate committee of…

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: A group has 12 members. In how many ways can 4 officers consisting of president , vice-president ,…

A: Total members n=12 no of officers r=4 Total no of ways=?

Q: A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated…

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Q: 10) If a man can select one of 4 shirts, one of 3 pairs of trousers and one of 2 pairs of shoes, how…

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Q: A basketball team contains 20 players. If 5 people can be on the court at one time, how many…

A: Total number of players is 20. The number of player to be court at one time is 5.

Q: A fast-food restaurant offers a special luncheon menu consisting of a sandwich, French fries, and a…

A: Given, A fast-food restaurant offers a special luncheon menu consisting of a sandwich, French fries,…

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: A veterinarian surveys 28 of his patrons.  He discovers that 12 have dogs, 10 have cats, and 6 have…

A:

Q: A company has 7 male and 12 female employees, and needs to nominate 2 men and 2 women for the…

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Q: A boy owns 2 pairs of pants, 7 shirts, 4 ties, and 5 jackets. How many different outfits can he wear…

A:

Q: A restaurant offers a 4 kinds of soup, 7 kinds of main dish, 5 kinds of vegetable dish, and 6 kinds…

A: A restaurant offers a 4 kinds of soup, 7 kinds of main dish, 5 kinds of vegetable dish, and 6 kinds…

Q: If there are five different toy cars, and you want to put fifteen toy cars on the display, how many…

A: Permutation is the measurement of principle counting. It is measure that arrange the data in an…

Q: A school dance committee is made up of 2 freshman, 3 sophomores, 3 juniors, and 5 seniors. How many…

A: The total number of members in the committee is 2+3+3+5=13. The number of freshmen (F), sophomores…

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.