(a) In a certain state, license plates have two letters followed by four digits. How many such license plates are possible? (b) If the state department of transportation decides to change the plates to have four letters followed by two digits. How many plates will now be possible?

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A: Explanation of the answer is as follows

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A: The phone number takes :  the form of a 3-digit area code Total digits possible = 10…

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A: 4 (a) There are totally 16 people out of which 7 are men and 9 are women. The committee should…

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Q: A license plate in a certain state consists of a letter followed by three numbers followed by two…

A: The license plate has combination like follows  A-XXX-AA where A is the letter and X is the number…

Q: . In an art class, the students are asked to create a 2D artwork using only the crayons they are…

A: We have to take out 4 from 24. So we will apply combination.

Q: There are 15 married couples in a dressing room. The photographer is tasked to take a picture of…

A: We need to find the number of people who must be called out of the room so that he is sure that…

Q: 5. a) How many ways can 6 people be lined up to get on a bus? b) If a certain 3 persons insist on…

A:

Q: Each student at State College has a student I.D. number consisting of seven digits (the first digit…

A: no.of digits ( 0 to 9)=10no.of letters(A,B,C,D,E)=5

Q: 1. Your professor has 10 advanced statistics texts and 8 advanced calculus texts. (a) How many ways…

A:

Q: (g) A company has two employees with 12 offices. How many ways are there to assign different offices…

A:

Q: (a). Three boys and three girls are seated at the round table. How many different arrangements are…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: (ii) exactly ten buses arrive from 5.00 pm to 6.30 pm, and three buses arrive from 6.30 pm to 7 pm?

A: please do (ii) only .   In one hour time, average number of buses leaving station A = 12  then , In…

Q: A small combination lock on a suitcase has 4 wheels, each labeled with the 10 digits 0 to 9 How many…

A: It is given that, a small combination lock on a suitcase has 4 wheels, each labeled with the 10…

Q: With a short time remaining in the day, a delivery driver has time to make deliveries at 5 locations…

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Q: Students are building their schedules at a small university. There are 12 departments offering…

A: There are 12 departments offering classes. A students have to build a schedule of 5 courses each…

Q: Peter has one of each of the following coins in his pocket: a penny, a nickel, a dollar. Four of the…

A: Given is Peter has one of each of the following coins in his pocket. a dime dollar. a a penny, a…

Q: license plates contain 3 letters followed by 4 digits. a. how many license plates are possible? b.…

A:

Q: Phone numbers consist of a three-digit area code followed by seven digits. If the area code must…

A:

Q: 13. Bill and Sue both work a night shift. Bill has every seventh night off and Sue has every fourth…

A:

Q: To use an automated teller machine at a certain​ bank, you must enter a 6​-digit ​code, using the…

A: To find-  Possible 6 digit codes if repetition of digits are permitted.

Q: 3n couples and their one child sit at a round table in such a way that their one child is between a…

A: It is given that there are 3n couples and their one child sit at a round table in such a way that…

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Q: 6. A question paper has two parts P and Q, each containing 10 questions. If a student needs to…

A:

Q: Each student at State College has a student I.D. number consisting of eight digits (the first digit…

A:

Q: 5. a) How many ways can 6 people be lined up to get on a bus?  b) If a certain 3 persons insist on…

A: Given numbers of people. 6 people

Q: 30. The number of floats in the last Panagbenga Festival is about 50. This year, it is expected that…

A: here given , The number of floats in the last Panagbenga Festival is about 50. This year, it is…

Q: (a) In a certain state, license plates have two letters followed by four digits. How many such…

A:

Q: 3- Practiôns 7 At a pet store, 10 of the puppies are black and of the puppies are 10 white. If you…

A:

Q: A state makes license plates with three letters followed by two numbers with no repetitions of the…

A: In general, the number of letters from A to Z is 26 and the number of digits from 0 to 9 is 10.

Q: A group of ten people are attending the movies together. (a) Two of the ten insist on sitting…

A: Given that, a group of ten people are attending the movies together. a) Given that, two of the ten…

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A:

Q: A jar is to be filled with 100 jelly beans. There are five varieties of beans to choose from and we…

A: As per given by the question,  The total number of jelly beans that is filled in the jar is 100.…

Q: In a college mathematics class, all the students are also taking anthropology, history or…

A: a) Assume that event A defines the students are taking anthropology, event H defines that students…

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Q: 2- The Swansons are planning to fly to Hawaii from Toronto with a stopover in Los Angeles. There are…

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Q: Non-personalized California license plates start with a nonzero digit (1-9) followed by three…

A: Total number of digits = 1 to 9 =9Total number of digits = 0 to 9 =10Total letters = 26

Q: a. If a coin is tossed nine ​times, how many different outcomes are​ possible? b. If a four​-sided…

A: Given a. If a coin is tossed nine timesb. If a four-sided die is tossed nine

Q: (b) A class of 18 students is divided into 3 groups of four students and 2 groups of three students.…

A: As per given by the question, A class of 18 student is divided into three groups of four student and…

Q: How many possible ways can a housewife take to buy a book from a bookstore, then buy groceries from…

A:

Q: Professor Bartlett teaches a class of 10 students. She has a visually challenged student, Louise,…

A: Given: Professor Bartlett teaches a class of 10 students. She has a visually challanged…

Q: 4. (a) In a group of 8 people, some of them shake hands. Is it possible that everyone shaked hands…

A:

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

A: Step 1

Q: Phone Numbers Current rules for telephone area codes allow the use of digits 2–9 for the first…

A: The fundamental counting rule statte that, If the first event could occur in m ways and he second…

Q: A student is to answer 10 out of 13 questions on an exam. (i) How many if he must answer exactly 3…

A: It is an important part of statistics . It is widely used .

Q: . a) How many ways can 6 people be lined up to get on a bus? o) If a certain 3 persons insist on…

A:

Q: 7 (a) Seven men and five women need to sit down for dinner at a circular table. (1) In how many ways…

A: Given that, Seven men and five women need to sit down for dinner at a circular table. We need to…

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.