Question 1

A computer dating service uses the results of its compatibility survey for arranging dates. The survey consists of 45 questions, each having five possible answers. How many different responses are possible if every question is answered?

Accepted Answer

The answer of A computer dating service uses the results...

Question 2

Four commuter trains and two express buses depart from city A to city B in the morning, and three commuter trains and two express buses operate on the return trip in the evening. In how many ways can a commuter from city A to city B complete a daily round trip via bus and/or train?
​
__________ possible ways

Accepted Answer

The answer of Four commuter trains and two express buses...

Question 3

In a state lottery there are 18 finalists eligible for the Big Money Draw. In how many ways can the first, second, and third prizes be awarded if no ticket holder may win more than one prize?
​
__________ different selections

Accepted Answer

The answer of In a state lottery there are 18...

Question 4

In recent years, the state of California issued license plates using a combination of one letter of the alphabet followed by two digits, followed by another three letters of the alphabet. How many different license plates can be issued using this configuration?
​
__________ different license plates

Accepted Answer

The answer of In recent years, the state of California...

Question 5

Two soups, four entrees, and four desserts are listed on the ''Special'' menu at the Neptune Restaurant. How many different selections consisting of one soup, one entree, and one dessert can a customer choose from this menu?
__________ different selections
​

Accepted Answer

The answer of Two soups, four entrees, and four desserts...

Question 6

An opinion poll is to be conducted among cable TV viewers. Four multiple-choice questions, each with three possible answers, will be asked. In how many different ways can a viewer complete the poll if exactly one response is given to each question?
​
__________ different ways

Accepted Answer

The answer of An opinion poll is to be conducted...

Question 7

How many international direct-dialing numbers are possible if each number consists of a four-digit area code (the first digit of which must be nonzero) and a five-digit telephone numbers (the first digit must be nonzero)? ​
A) 1,053,000,000
B) 486,000,000
C) 810,000,000
D) 729,000,000
E) 567,000,000

Accepted Answer

For the four-digit area code, the first digit must be nonzero, which means there are 9 choices (1-9). For the remaining three digits, there are 10 choices (0-9) for each digit, giving us a total of 9x10x10x10 = 9,000 possible area codes.

For the five-digit telephone number, the first digit must be nonzero, which again gives us 9 choices. The remaining four digits can again be any of the 10 digits (0-9). This gives us a total of 9x10x10x10x10 = 90,000 possible telephone numbers.

To get the total number of combinations, we multiply the number of possible area codes by the number of possible telephone numbers: 9,000 x 90,000 = 810,000,000. Therefore, the correct answer is option C.

Question 8

Four different types of monthly commuter passes are offered by a city's local transit authority for three different groups of passengers. How many different kinds of passes must be possible?
​
__________ possible passes

Accepted Answer

The answer of Four different types of monthly commuter passes...

Question 9

​How many two-letter code words can be constructed from the first ten letters of the Greek alphabet if no repetitions are allowed?
__________ code words

Accepted Answer

The answer of ​How many two-letter code words can be...

Question 10

Student Painters, which specializes in painting the exterior of residential buildings, has seven people available to be organized into four-person and three-person teams. ​
In how many ways can the four-person team be formed?
A) 504
B) 840
C) 1,260
D) 1,092
E) 756

Accepted Answer

The answer of Student Painters, which specializes in painting the...

Question 11

​An automobile manufacturer has three different subcompact cars in the line. Customers selecting one of these cars have a choice of three engine sizes, four body styles, and three color schemes. How many different selections can a customer make?
__________ different selections

Accepted Answer

The answer of ​An automobile manufacturer has three different subcompact...

Question 12

Student Painters, which specializes in painting the exterior of residential buildings, has six people available to be organized into two-person and four-person teams.
​
In how many ways can the two-person team be formed?
__________
​
In how many ways can the four-person team be formed?
__________
​
In how many ways can the company organize the available people into two- or four-person teams?

Accepted Answer

The answer of Student Painters, which specializes in painting the...

Question 13

Over the years one state has used different combinations of letters of the alphabet and digits on its automobile license plates. At one time, license plates were issued that consisted of three letters followed by three digits. How many different license plates can be issued under this arrangement?
​
__________ different license plates

Accepted Answer

The answer of Over the years one state has used...

Question 14

In a survey conducted by a union, members were asked to rate the importance of the following issues: (1) job security, (2) increased fringe benefits, and (3) improved working conditions. Three different responses were allowed for each issue. Among completed surveys, how many different responses to this survey were possible?
​
__________ different responses

Accepted Answer

The answer of In a survey conducted by a union,...

Question 15

A coin is tossed 5 times and the sequence of heads and tails is recorded. Use the generalized multiplication principle to determine the number of outcomes of this activity.
__________ possible outcomes

Accepted Answer

The answer of A coin is tossed 5 times and...

Question 16

​A warranty identification number for a certain product consists of a letter of the alphabet followed by a two-digit number. How many possible identification numbers are there if the first digit of the two-digit number must be nonzero?
__________ numbers
​

Accepted Answer

The answer of ​A warranty identification number for a certain...

Question 17

A new state employee is offered a choice of nine basic health plans, two dental plans, and three vision care plans. How many different health-care plans are there to choose from if one plan is selected from each category?
​
__________ different plans

Accepted Answer

The answer of A new state employee is offered a...

Question 18

How many seven-digit telephone numbers are possible if the first digit must be nonzero?
​
__________
​
How many international direct-dialing numbers are possible if each number consists of a four-digit area code (the first digit of which must be nonzero) and a number of the type described in part (a)?
​
__________

Accepted Answer

The answer of How many seven-digit telephone numbers are possible...

Question 19

A female executive selecting her wardrobe purchased three blazers, five blouses, and four skirts in coordinating colors. How many ensembles consisting of a blazer, a blouse, and a skirt can she create from this collection?
​
__________ possible ensembles

Accepted Answer

The answer of A female executive selecting her wardrobe purchased...

Question 20

​Computers manufactured by a certain company have a serial number consisting of a letter of the alphabet followed by a six-digit number. If all the serial numbers of this type have been used, how many sets have already been manufactured?
__________ sets

Accepted Answer

The answer of ​Computers manufactured by a certain company have...

Quiz 6: Sets and Counting

A computer dating service uses the results of its compatibility survey for arranging dates. The survey consists of 45 questions, each having five possible answers. How many different responses are possible if every question is answered?

In a state lottery there are 18 finalists eligible for the Big Money Draw. In how many ways can the first, second, and third prizes be awarded if no ticket holder may win more than one prize? __________ different selections

In recent years, the state of California issued license plates using a combination of one letter of the alphabet followed by two digits, followed by another three letters of the alphabet. How many different license plates can be issued using this configuration? __________ different license plates

Two soups, four entrees, and four desserts are listed on the ''Special'' menu at the Neptune Restaurant. How many different selections consisting of one soup, one entree, and one dessert can a customer choose from this menu? __________ different selections

An opinion poll is to be conducted among cable TV viewers. Four multiple-choice questions, each with three possible answers, will be asked. In how many different ways can a viewer complete the poll if exactly one response is given to each question? __________ different ways

How many international direct-dialing numbers are possible if each number consists of a four-digit area code (the first digit of which must be nonzero) and a five-digit telephone numbers (the first digit must be nonzero) ?

Four different types of monthly commuter passes are offered by a city's local transit authority for three different groups of passengers. How many different kinds of passes must be possible? __________ possible passes

How many two-letter code words can be constructed from the first ten letters of the Greek alphabet if no repetitions are allowed? __________ code words

Student Painters, which specializes in painting the exterior of residential buildings, has seven people available to be organized into four-person and three-person teams. In how many ways can the four-person team be formed?

An automobile manufacturer has three different subcompact cars in the line. Customers selecting one of these cars have a choice of three engine sizes, four body styles, and three color schemes. How many different selections can a customer make? __________ different selections

A coin is tossed 5 times and the sequence of heads and tails is recorded. Use the generalized multiplication principle to determine the number of outcomes of this activity. __________ possible outcomes

A warranty identification number for a certain product consists of a letter of the alphabet followed by a two-digit number. How many possible identification numbers are there if the first digit of the two-digit number must be nonzero? __________ numbers

A new state employee is offered a choice of nine basic health plans, two dental plans, and three vision care plans. How many different health-care plans are there to choose from if one plan is selected from each category? __________ different plans

How many seven-digit telephone numbers are possible if the first digit must be nonzero? How many international direct-dialing numbers are possible if each number consists of a four-digit area code (the first digit of which must be nonzero) and a number of the type described in part (a)?

A female executive selecting her wardrobe purchased three blazers, five blouses, and four skirts in coordinating colors. How many ensembles consisting of a blazer, a blouse, and a skirt can she create from this collection? __________ possible ensembles

Computers manufactured by a certain company have a serial number consisting of a letter of the alphabet followed by a six-digit number. If all the serial numbers of this type have been used, how many sets have already been manufactured? __________ sets

Quiz 6: Sets and Counting

A computer dating service uses the results of its compatibility survey for arranging dates. The survey consists of 45 questions, each having five possible answers. How many different responses are possible if every question is answered?

In a state lottery there are 18 finalists eligible for the Big Money Draw. In how many ways can the first, second, and third prizes be awarded if no ticket holder may win more than one prize? ​ __________ different selections

Two soups, four entrees, and four desserts are listed on the ''Special'' menu at the Neptune Restaurant. How many different selections consisting of one soup, one entree, and one dessert can a customer choose from this menu? __________ different selections ​

An opinion poll is to be conducted among cable TV viewers. Four multiple-choice questions, each with three possible answers, will be asked. In how many different ways can a viewer complete the poll if exactly one response is given to each question? ​ __________ different ways

How many international direct-dialing numbers are possible if each number consists of a four-digit area code (the first digit of which must be nonzero) and a five-digit telephone numbers (the first digit must be nonzero) ? ​

Four different types of monthly commuter passes are offered by a city's local transit authority for three different groups of passengers. How many different kinds of passes must be possible? ​ __________ possible passes

​How many two-letter code words can be constructed from the first ten letters of the Greek alphabet if no repetitions are allowed? __________ code words

Student Painters, which specializes in painting the exterior of residential buildings, has seven people available to be organized into four-person and three-person teams. ​ In how many ways can the four-person team be formed?

​An automobile manufacturer has three different subcompact cars in the line. Customers selecting one of these cars have a choice of three engine sizes, four body styles, and three color schemes. How many different selections can a customer make? __________ different selections

A coin is tossed 5 times and the sequence of heads and tails is recorded. Use the generalized multiplication principle to determine the number of outcomes of this activity. __________ possible outcomes

​A warranty identification number for a certain product consists of a letter of the alphabet followed by a two-digit number. How many possible identification numbers are there if the first digit of the two-digit number must be nonzero? __________ numbers ​

A new state employee is offered a choice of nine basic health plans, two dental plans, and three vision care plans. How many different health-care plans are there to choose from if one plan is selected from each category? ​ __________ different plans

A female executive selecting her wardrobe purchased three blazers, five blouses, and four skirts in coordinating colors. How many ensembles consisting of a blazer, a blouse, and a skirt can she create from this collection? ​ __________ possible ensembles

​Computers manufactured by a certain company have a serial number consisting of a letter of the alphabet followed by a six-digit number. If all the serial numbers of this type have been used, how many sets have already been manufactured? __________ sets

In a state lottery there are 18 finalists eligible for the Big Money Draw. In how many ways can the first, second, and third prizes be awarded if no ticket holder may win more than one prize? __________ different selections

Two soups, four entrees, and four desserts are listed on the ''Special'' menu at the Neptune Restaurant. How many different selections consisting of one soup, one entree, and one dessert can a customer choose from this menu? __________ different selections

An opinion poll is to be conducted among cable TV viewers. Four multiple-choice questions, each with three possible answers, will be asked. In how many different ways can a viewer complete the poll if exactly one response is given to each question? __________ different ways

How many international direct-dialing numbers are possible if each number consists of a four-digit area code (the first digit of which must be nonzero) and a five-digit telephone numbers (the first digit must be nonzero) ?

Four different types of monthly commuter passes are offered by a city's local transit authority for three different groups of passengers. How many different kinds of passes must be possible? __________ possible passes

How many two-letter code words can be constructed from the first ten letters of the Greek alphabet if no repetitions are allowed? __________ code words

Student Painters, which specializes in painting the exterior of residential buildings, has seven people available to be organized into four-person and three-person teams. In how many ways can the four-person team be formed?

An automobile manufacturer has three different subcompact cars in the line. Customers selecting one of these cars have a choice of three engine sizes, four body styles, and three color schemes. How many different selections can a customer make? __________ different selections

A warranty identification number for a certain product consists of a letter of the alphabet followed by a two-digit number. How many possible identification numbers are there if the first digit of the two-digit number must be nonzero? __________ numbers

A new state employee is offered a choice of nine basic health plans, two dental plans, and three vision care plans. How many different health-care plans are there to choose from if one plan is selected from each category? __________ different plans

A female executive selecting her wardrobe purchased three blazers, five blouses, and four skirts in coordinating colors. How many ensembles consisting of a blazer, a blouse, and a skirt can she create from this collection? __________ possible ensembles

Computers manufactured by a certain company have a serial number consisting of a letter of the alphabet followed by a six-digit number. If all the serial numbers of this type have been used, how many sets have already been manufactured? __________ sets