Question 1

Let U denote the set of all senators in Congress. Let
​   ​
Write the set that represents the following statement:
​
The set of all Democrats who are lawyers.

Accepted Answer

The answer of Let U denote the set of all...

Question 2

In how many ways can seven different books arranged on a shelf? ​

Accepted Answer

A)  5,040 
B)  49 
C)  14 
D)  5,050 
E)  720 
A)  5,040 
B)  49 
C)  14 
D)  5,050 
E)  720 A

Question 3

A 2-member executive committee is to be formed from a 12-member board of directors. In how many ways can it be formed? ​

Accepted Answer

A)  2 
B)  24 
C)  66 
D)  71 
E)  132 
A)  2 
B)  24 
C)  66 
D)  71 
E)  132 C

Question 4

A quorum (minimum) of 9 voting members is required at all meetings of some association. If there is a total of 15 voting members in the group, find the number of ways this quorum can be formed. ​

Accepted Answer

A)  5,005 
B)  5,012 
C)  5,017 
D)  5,020 
E)  5,008 
A)  5,005 
B)  5,012 
C)  5,017 
D)  5,020 
E)  5,008

Question 5

Evaluate the expression. ​   ​

Accepted Answer

A)  136 
B)  129 
C)  126 
D)  123 
A)  136 
B)  129 
C)  126 
D)  123

Question 6

In a survey of 300 individual investors regarding subscriptions to the New York Times (NYT), Wall Street Journal (WSJ), and USA Today (UST), the following data were obtained: ​
122 subscribe to the NYT.
​
151 subscribe to the WSJ.
​
63 subscribe to the UST.
​
39 subscribe to the NYT and WSJ.
​
29 subscribe to the WSJ and UST.
​
18 subscribe to the NYT and UST.
​
35 do not subscribe to any of these newspapers.
​
How many subscribe to only one of these newspapers?
​

Accepted Answer

A)  244 
B)  229 
C)  179 
D)  209 
E)  194 
A)  244 
B)  229 
C)  179 
D)  209 
E)  194

Question 7

To gain access to his account, a customer using an automatic machine (ATM) must enter a five-digit code. If repetition of same five digit is not allowed (for example, 55555), how many possible combinations are there?

Accepted Answer

A)  9,990 
B)  99,990 
C)  6,551 
D)  120 
E)  240 
A)  9,990 
B)  99,990 
C)  6,551 
D)  120 
E)  240

Question 8

Weaver and Kline, a stock brokerage firm, has received six inquiries regarding new accounts. In how many ways can these inquiries be directed to its 15 account executives if each executive handles no more than one inquiry?
​
__________ ways

Accepted Answer

The answer of Weaver and Kline, a stock brokerage firm,...

Question 9

A survey of 1,200 subscribers to the Los Angeles Times revealed that 1,000 people subscribe to the daily morning edition and 500 subscribe to both the daily and the Sunday editions. How many subscribe to the Sunday edition? How many subscribe to the Sunday edition only?
​
__________ subscribes to the Sunday edition
​
__________ subscribes to the Sunday edition only

Accepted Answer

The answer of A survey of 1,200 subscribers to the...

Question 10

Let   . Which of the following sets are equal to A?
​

Accepted Answer

The answer of Let   . Which of the...

Question 11

Weaver and Kline, a stock brokerage firm, has received six inquiries regarding new accounts. In how many ways can these inquiries be directed to its 12 account executives if each executive handles no more than one inquiry? ​

Accepted Answer

A)  665,306 
B)  665,288 
C)  665,293 
D)  665,228 
E)  665,280 
A)  665,306 
B)  665,288 
C)  665,293 
D)  665,228 
E)  665,280

Question 12

Let U denote the set of all employees in a hospital. Let ​           ​
Describe the set in words.
​   ​

Accepted Answer

A)  The set of all employees in a hospital who are male doctors. 
B)  The set of all employees in a hospital who are male administrators. 
C)  The set of all employees in a hospital who are female doctors. 
D)  The set of all employees in a hospital who are female administrators. 
E)  The set of all employees in a hospital who are both doctors and administrators. 
A)  The set of all employees in a hospital who are male doctors. 
B)  The set of all employees in a hospital who are male administrators. 
C)  The set of all employees in a hospital who are female doctors. 
D)  The set of all employees in a hospital who are female administrators. 
E)  The set of all employees in a hospital who are both doctors and administrators.

Question 13

Evaluate the expression. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

Write the following set in builder notation form. The set gold medalists in the   Winter Olympic Games.
​

Accepted Answer

A)  {x = x is a gold medalist in the   Winter Olympic Games} 
B)  {x is a gold medalist in the Olympic Games} 
C)  {x | x is a gold medalist in the   Winter Olympic Games} 
D)  {x is a gold medalist in the   Winter Olympic Games} 
E)  {x is a player in the Olympic Games} 
A)  {x = x is a gold medalist in the   Winter Olympic Games} 
B)  {x is a gold medalist in the Olympic Games} 
C)  {x | x is a gold medalist in the   Winter Olympic Games} 
D)  {x is a gold medalist in the   Winter Olympic Games} 
E)  {x is a player in the Olympic Games}

Question 15

Let A, B, and C be subsets of a universal set U and suppose   ,   ,   ,   ,   ,   ,   , and   . ​
Compute   .
​

Accepted Answer

A)  38 
B)  33 
C)  19 
D)  24 
E)  34
F) 9 
A)  38 
B)  33 
C)  19 
D)  24 
E)  34
F) 9

Question 16

​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 17

In a card game, a 2-card hand consisting of an ace and either a face card   or a 10 is called a "win". If a standard 52-card deck is used, determine how many winning hands can be dealt.(A "face card" is a jack, queen, or king.)

Accepted Answer

A)  48 
B)  28 
C)  20 
D)  16 
E)  40 
A)  48 
B)  28 
C)  20 
D)  16 
E)  40

Question 18

A student planning her curriculum for the upcoming year must select one of five Business courses, one of seven Mathematics courses, two of four elective courses, and either one of three History courses or one of four Social Science courses. How many different curricula are available for her consideration?
​
__________ different curricula

Accepted Answer

The answer of A student planning her curriculum for the...

Question 19

Refer to the accompanying figure and find the points that belong to the set. ​   ​   ​

Accepted Answer

A)  r 
B)  s, t 
C)  x, y 
D)  v 
E)    
A)  r 
B)  s, t 
C)  x, y 
D)  v 
E)

Question 20

How many two-digit numbers can be formed by using the numerals in the set {1,4,6,8,9} if repetition is not allowed? ​

Accepted Answer

A)  20 
B)  118 
C)  2 
D)  22 
E)  10 
A)  20 
B)  118 
C)  2 
D)  22 
E)  10

Let U denote the set of all senators in Congress. Let Write the set that represents the following statement: The set of all Democrats who are lawyers.

In how many ways can seven different books arranged on a shelf?

A 2-member executive committee is to be formed from a 12-member board of directors. In how many ways can it be formed?

A quorum (minimum) of 9 voting members is required at all meetings of some association. If there is a total of 15 voting members in the group, find the number of ways this quorum can be formed.

Evaluate the expression.

To gain access to his account, a customer using an automatic machine (ATM) must enter a five-digit code. If repetition of same five digit is not allowed (for example, 55555), how many possible combinations are there?

Weaver and Kline, a stock brokerage firm, has received six inquiries regarding new accounts. In how many ways can these inquiries be directed to its 15 account executives if each executive handles no more than one inquiry? __________ ways

Let . Which of the following sets are equal to A?

Weaver and Kline, a stock brokerage firm, has received six inquiries regarding new accounts. In how many ways can these inquiries be directed to its 12 account executives if each executive handles no more than one inquiry?

Let U denote the set of all employees in a hospital. Let Describe the set in words.

Evaluate the expression.

Write the following set in builder notation form. The set gold medalists in the Winter Olympic Games.

Let A, B, and C be subsets of a universal set U and suppose , , , , , , , and . Compute .

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

In a card game, a 2-card hand consisting of an ace and either a face card or a 10 is called a "win". If a standard 52-card deck is used, determine how many winning hands can be dealt.(A "face card" is a jack, queen, or king.)

Refer to the accompanying figure and find the points that belong to the set.

How many two-digit numbers can be formed by using the numerals in the set {1,4,6,8,9} if repetition is not allowed?

Straight Lines and Linear Functions

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Exam 6: Sets and Counting

Let U denote the set of all senators in Congress. Let ​ ​ Write the set that represents the following statement: ​ The set of all Democrats who are lawyers.

In how many ways can seven different books arranged on a shelf? ​

A 2-member executive committee is to be formed from a 12-member board of directors. In how many ways can it be formed? ​

A quorum (minimum) of 9 voting members is required at all meetings of some association. If there is a total of 15 voting members in the group, find the number of ways this quorum can be formed. ​

Evaluate the expression. ​ ​

To gain access to his account, a customer using an automatic machine (ATM) must enter a five-digit code. If repetition of same five digit is not allowed (for example, 55555), how many possible combinations are there?

Weaver and Kline, a stock brokerage firm, has received six inquiries regarding new accounts. In how many ways can these inquiries be directed to its 15 account executives if each executive handles no more than one inquiry? ​ __________ ways

Let . Which of the following sets are equal to A? ​

Weaver and Kline, a stock brokerage firm, has received six inquiries regarding new accounts. In how many ways can these inquiries be directed to its 12 account executives if each executive handles no more than one inquiry? ​

Let U denote the set of all employees in a hospital. Let ​ ​ Describe the set in words. ​ ​

Evaluate the expression. ​ ​

Write the following set in builder notation form. The set gold medalists in the Winter Olympic Games. ​

Let A, B, and C be subsets of a universal set U and suppose , , , , , , , and . ​ Compute . ​

​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

In a card game, a 2-card hand consisting of an ace and either a face card or a 10 is called a "win". If a standard 52-card deck is used, determine how many winning hands can be dealt.(A "face card" is a jack, queen, or king.)

Refer to the accompanying figure and find the points that belong to the set. ​ ​ ​

How many two-digit numbers can be formed by using the numerals in the set {1,4,6,8,9} if repetition is not allowed? ​

Straight Lines and Linear Functions

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Let U denote the set of all senators in Congress. Let Write the set that represents the following statement: The set of all Democrats who are lawyers.

In how many ways can seven different books arranged on a shelf?

A 2-member executive committee is to be formed from a 12-member board of directors. In how many ways can it be formed?

A quorum (minimum) of 9 voting members is required at all meetings of some association. If there is a total of 15 voting members in the group, find the number of ways this quorum can be formed.

Evaluate the expression.

Weaver and Kline, a stock brokerage firm, has received six inquiries regarding new accounts. In how many ways can these inquiries be directed to its 15 account executives if each executive handles no more than one inquiry? __________ ways

Let . Which of the following sets are equal to A?

Weaver and Kline, a stock brokerage firm, has received six inquiries regarding new accounts. In how many ways can these inquiries be directed to its 12 account executives if each executive handles no more than one inquiry?

Let U denote the set of all employees in a hospital. Let Describe the set in words.

Evaluate the expression.

Write the following set in builder notation form. The set gold medalists in the Winter Olympic Games.

Let A, B, and C be subsets of a universal set U and suppose , , , , , , , and . Compute .

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

Refer to the accompanying figure and find the points that belong to the set.

How many two-digit numbers can be formed by using the numerals in the set {1,4,6,8,9} if repetition is not allowed?