Telephone Numbers   In the past, a local telephone number in a country consisted of a sequence of four letters followed by five digits. Three letters were associated with each number from 2 to 9 (just as in the standard telephone layout

Q: horse race, eight horses are running. Assume you have purchased a Trifecta ticket. (In Trifecta, the…

A: Here we want to Know possibilities of a Trifecta exist?

Q: In an apartment complex with 11 mailboxes in how many ways can a mail carrier distribute 11 letters…

A: Consider the given information.

Q: Telephone Numbers. In the United States, telephone numbers consist of a three-digit area code…

A: a. Computation of number of possible different area codes:The number of possible different area…

Q: Ten passengers get on a shuttle at the airport. The shuttle has a route that includes 5 hotels, and…

A: There are 10 passengers get on a shuttle at the airport. The shuttle has a route that includes 5…

Q: 14. One day, Hannah starts a new online Internet club by convincing two of her friends to join. The…

A: The key concept is that on any day if they are n members they will convince to join 2n more members…

Q: Donald is making a salad at Sweet Tomatoes.  His salad can consist of just lettuce, or he can add…

A:

Q: 36. Holiday Photos A couple have seven children: three girls and four boys. In how many ways can the…

A: Given that: the couple have seven children, three girls and four boys. To find: the number of ways…

Q: A certain identification number is a sequence of five digits. (a) How many identification numbers…

A:

Q: Car Engines In an eight-cylinder V8 engine, the even-numbered cylinders are on the left and the…

A: Consider the provided question, (a) We need to find the number of possible good firing sequence.…

Q: 20 applicants from a pool of 90 applications will be hired. How many ways are there to select the…

A: There are total 90 applications and we have to select 20 applicants.   So we have to find the number…

Q: Telephone Numbers In the past, a local telephone number in a country consisted of a sequence of…

A: A local telephone number in a country consisted of a sequence of three letters followed by four…

Q: Eight friends on bicycles find an empty bike rack with exactly eight spots for bikes. How many ways…

A: Adya and Moira can park at the ends in 2!=2 ways.  When the ends are occupied then (8-2)=6 spots…

Q: how many passwords are there if you do not allow repeating digits? b.) How many passwords are there…

A: Since , the passwords are made by using 4 digits from 1-9. Total numbers=9 Password length=4 Our aim…

Q: How many different three-letter sequences can you make by rearranging the letters {J,A,C,K}?…

A: If we have so many things then we arrange those in a certain order, or without order. But we arrange…

Q: A jar contains 40 balls numbered 1 through 40. Three balls are removed without being returned to the…

A: Using permutation and combinations we can solve for the number of sequences possible

Q: A phone has 8 ring tones in memory. Every morning the cell plays three tones in sequence. Find how…

A: Given Total number of ringtones in memory (n) = 8 Number of tones in sequence (r) = 3 Now, number…

Q: A gold, a silver, and a bronze medal are awarded in an Olympic event. In how many possible ways can…

A: Consider the number of winners is 11. Consider the number of possibilities of silver is 11. The…

Q: n the first day of vacation, you read one-quarter of a novel. On the second day, you read half of…

A: Given: To explain the given statement as follows, To find the total pages that the novel has and…

Q: 700 people went to the amusement park. 500 of them went on a roller-coaster, 100 of them went to the…

A: Let R=roller coaster  H=Haunted house W=water slides S=total 700 people Given, 2 people went on all…

Q: ternary digit is either 0, 1, or 2. How many sequences of seven ternary digits are possible…

A:

Q: Until recently, all area codes had a 0 or a 1 as the middle digit and the first digit could not be 0…

A: Given: All area code has 0 or 1 as a middle digit and first digit could not be 0 or 1 and third…

Q: Six performers are to present their comedy acts on a weekend evening at a comedy club. One of the…

A: We can pick the last position in 1 way only.  When the last position is fixed then we can select the…

Q: A gold, a silver, and a bronze medal are awarded in an Olympic event. In how many possible ways can…

A: It is given that there are three kinds of medals, and the medals will be distributed between 14…

Q: In a sequence of numbers, az3 = 0, a4 = 4, a5 = 8, a6 = 12, and a7 = 16. Based on this information,…

A: According to the given condition a3=0, substitute 3 for n in all the equations.

Q: Ten different people walk into a delicatessen to buy a Four always order tuna fish, two always order…

A: a)The number of different sequences of sandwiches possible is obtained below: From the information,…

Q: Telephone Area Codes Several years ago, the United States began running out of telephone numbers.…

A: Given:  The telephone number has 7 digits.  (3 digit sequence + 4 digit sequence)  The first 3 digit…

Q: A clerk at a bookstore is restocking a shelf of the best-selling novels. He has four copies each of…

A: Given: A clerk at a bookstore is restocking a shelf of the best-selling novels. He has four copies…

Q: 1. Three-digit numbers (a) How many repeating three-digit numbers can be formed using the numbers…

A:

Q: Eight people are going for a ride in a boat that seats eight people. One person will drive, and only…

A: Given an eight seater boat. We need to find number of seating arrangements possible for 8 people…

Q: Car Engines   In an eight-cylinder V8 engine, the even-numbered cylinders are on the left and the…

A: (a) It is required to find the number of possible good firing sequence. According to the…

Q: Committee: The Student Council at a certain school has seven members. Four members will form an…

A: Given that  Total member=n=7 Position filled=k=4 How many ways can these four positions be filled

Q: A ternary digit is either 0, 1, or 2. How many sequences of seven ternary digits are possible…

A: Given: A ternary digit is either 0,1, or 2. To find: We need the number of sequence of seven ternary…

Q: Finite Math   You have 7 math books and 7 history books to put on a shelf with five slots. In how…

A: There are several powerful methods for counting objects and sets of objects without actually having…

Q: Telephone Numbers In the past, a local telephone number in a country consisted of a sequence of…

A: There are 24 letter So the number of arrangements possible for three 3 letters out o 24 letters are…

Q: An ice cream store sells 27 flavors of ice cream. Determine the number of possible 7-dip sundaes.…

A:

Q: A legislative committee consists of 8 Democrats and 10 Republicans. A delegation of 4 is to be…

A: Solutions

Q: In a city, the bus route numbers consist of a natural number less than 100, followed one of the…

A: In a city, the bus route numbers consist of a natural number less than 100, followed one of the…

Q: clerk at a bookstore is restocking a shelf of the best-selling novels. He has three copies each of…

A:

Q: A freight train is going to carry four tankers, six coal cars, and ten lumber cars. How many…

A: It is given that, There are 4 tankers , 6 coal cars and 10  lumber cars.

Q: 32. License Plates A state has registered 8 million automobiles. To simplify the license plate…

A: Given: A state has registered 8 million automobiles. To find: the number of license plates that can…

Q: Number of Students: In a certain school 80% of the students in first-year chemistry have had…

A: Total number of students in first year chemistry is 280.In which, 80% students have had…

Q: Ten passengers get on an airport shuttle at the airport. The shuttle has a route that includes 5…

A:

Q: A problem in Mrs. Schrader's geometry class has seven steps in the proof. She writes the steps, one…

A: A problem in Mrs. Schrader's geometry class has seven steps in the proof. She writes the steps,…

Q: An algebra class has 12 students and 12 desks. For the sake of variety, students chang thhe seating…

A:

Q: Telephone Numbers In the past, a local telephone number in a country consisted of a sequence of two…

A: The Solution is given below

Q: At a meeting between coworkers, the eight participants sit on a round table facing the beach. There…

A: The number of ways in which n different objects can be arranged is given by n!, where…

Q: Using the roll of a six-sided die and the flip of a coin, in how many ways can you obtain a heads…

A: We have to find

Q: If you flip a coin 9 times, you get a sequence of Heads (H) and tails (T). (a) How many different…

A: Product rule : If one event can occur in m ways AND a second event can occur in n ways , then the…

Q: How many four-letter sequences are possible that use the letters q, u, a, k, e, s at most once each?

A: Use permutation and combination

Q: Morse Codes The International Morse code is a way of transmitting coded text by using sequences of…

A: The coded texts are transmitted by using sequences of on/off tones. Here, each segment is either a…