Question 1

List the set of all outcomes of tossing three indistinguishable coins.

Accepted Answer

$\{ ( \mathrm { T } , \mathrm { T } , \mathrm { T } ) , ( \mathrm { T } , \mathrm { T } , \mathrm { H } ) , ( \mathrm { H } , \mathrm { H } , \mathrm { T } ) , ( \mathrm { H } , \mathrm { H } , \mathrm { H } ) \}$

Question 2

A telephone number consists of a sequence of seven digits not starting with a 0 or a 1. How many phone numbers begin with either 7,342, 7,423, or 7,224  ?

Accepted Answer

A) 2,187 numbers 
B)  27,000 numbers 
C)  1,000 numbers 
D)  3,000 numbers 
E)  90 numbers 
A) 2,187 numbers 
B)  27,000 numbers 
C)  1,000 numbers 
D)  3,000 numbers 
E)  90 numbers D

Question 3

How many ordered sequences are possible that contain 2 objects chosen from 9

Accepted Answer

A)  72 
B)   5,040 
C)   2 
D)   725,760 
E)   36 
A)  72 
B)   5,040 
C)   2 
D)   725,760 
E)   36 A

Question 4

A test requires that you answer either Part A or Part B. Part A consists of 16 true-false questions and part B consists of 10 multiple-choice questions with one correct answer out of 3. How many different completed answer sheets are possible  ?

Accepted Answer

A) 65,566 sheets 
B)  1,966,080 sheets 
C)  59,081 sheets 
D)  960 sheets 
E)  124,585 sheets 
A) 65,566 sheets 
B)  1,966,080 sheets 
C)  59,081 sheets 
D)  960 sheets 
E)  124,585 sheets

Question 5

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 3 lavender marbles. How many sets of 3 marbles include none of the yellow marbles

Accepted Answer

A)  220 
B)   2 
C)   1,320 
D)   660 
E)   504 
A)  220 
B)   2 
C)   1,320 
D)   660 
E)   504

Question 6

A freelance computer consultant keeps a database of her clients, which contains the names  $S = \{ \text { Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global, Hilbert } \}$  
The following clients owe her money:
   $A = \{ \text { Acme, Crafts, Brothers, Global } \}$  
The following clients have employed her in the last year:
  $G = \{ \text { Acme, Crafts, Dion, Brothers, Global, Hilbert } \}$  
Find the clients who do not owe her money or have employed her in the last year.

Accepted Answer

A)  $\{ \text { Brothers, Acme, Crafts, Dion, Global, Hilbert\} }$ 
B)  $\{ \text { Acme, Brothers, Crafts, Global\} }$ 
C)  $\{ \text { Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global, Hilbert } \}$ 
D)  $\{ \text { Dion, Hilbert } \}$ 
E)  $\varnothing$ 
A)  $\{ \text { Brothers, Acme, Crafts, Dion, Global, Hilbert\} }$ 
B)  $\{ \text { Acme, Brothers, Crafts, Global\} }$ 
C)  $\{ \text { Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global, Hilbert } \}$ 
D)  $\{ \text { Dion, Hilbert } \}$ 
E)  $\varnothing$

Question 7

How many three-letter sequences are possible that contain only the letters R and D, with D occurring only once  ?

Accepted Answer

A) 4 sequences 
B)  27 sequences 
C)  9 sequences 
D)  6 sequences 
E)  3 sequences 
A) 4 sequences 
B)  27 sequences 
C)  9 sequences 
D)  6 sequences 
E)  3 sequences

Question 8

In a survey of 100 Enormous State University students, 23 enjoyed classical music, 22 enjoyed rock music, and 23 enjoyed house music. Only 7 of the students enjoyed both classical and rock. How many of those that enjoyed rock did not enjoy classical music  ?
__________ students enjoyed rock but not classical music.

Accepted Answer

The answer of In a survey of 100 Enormous State...

Question 9

In how many ways can a 5-card hand containing 4 kings and 1 queen be dealt from a deck of 52 cards

Accepted Answer

The answer of In how many ways can a 5-card...

Question 10

In a survey of 120 Enormous State University students, 22 enjoyed classical music, 24 enjoyed rock music, and 23 enjoyed house music. Only 6 of the students enjoyed both classical and rock. How many of those that enjoyed rock did not enjoy classical music  ?

Accepted Answer

A) 16 students 
B)  17 students 
C)  6 students 
D)  18 students 
E)  51 students 
A) 16 students 
B)  17 students 
C)  6 students 
D)  18 students 
E)  51 students

Question 11

A test requires that you answer first Part A and then either Part B or Part C. Part A consists of 7 true/false questions, Part B consists of 9 multiple choice questions with one correct answer out of 5, and Part C requires you to match 8 questions with 8 different answers. (Each question matches exactly one correct answer.) How many different completed answer sheets are possible  ?

Accepted Answer

A)  79,000,000,000 
B)  1,993,573 
C)   78,755,160,960 
D)   255,160,960 
E)   307,257,753,600 
A)  79,000,000,000 
B)  1,993,573 
C)   78,755,160,960 
D)   255,160,960 
E)   307,257,753,600

Question 12

Given that $A = \{ \mathrm { H } , \mathrm { T } \}$ , and $B = \{ 1,2,3,4,5,6 \}$ , and $C = \{ \text { red, green, blue } \}$ .
​
Find $n ( A \times B \times B )$ .
​ $n ( A \times B \times B ) =$ __________

Accepted Answer

The answer of Given that \(A = \{ \mathrm {...

Question 13

Given that $A = \{ \mathrm { H } , \mathrm { T } \}$ , $B = \{ 1,2,3,4,5 \}$ and $C = \{ \text { red, green, blue } \}$ . 
Find $n ( A \times B \times B )$ .

Accepted Answer

A) 30 
B)  12 
C)  50 
D)  10 
E)  48 
A) 30 
B)  12 
C)  50 
D)  10 
E)  48

Question 14

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 2 lavender marbles. How many sets of 4 marbles include at most one of the yellow marbles

Accepted Answer

The answer of A bag contains 3 red marbles, 6...

Question 15

Evaluate $\frac { 4 ! } { 1 ! }$ .
​ $\frac { 4 ! } { 1 ! } =$ __________

Accepted Answer

The answer of Evaluate \(\frac { 4 ! } {...

Question 16

Let $S = \{ \text { Bamsley, Manchester United, Southend, Sheffield United, Liverpool, Maroka Swallows, Witbank Aces, Royal Tigers, Dundee United, Lyon } \}$ be a universal set, $A = \{ \text { Southend, Witbank Aces, Maroka Swallows, Royal Tigers } \}$ , and $B = \{ \text { Sheffield United, Manchester United, Southend } \}$ . Find $n \left( ( A \cup B ) ^ { \prime } \right)$ .
  $n \left( ( A \cup B ) ^ { \prime } \right) =$ __________

Accepted Answer

The answer of Let \(S = \{ \text { Bamsley,...

Question 17

A Social Security number is a sequence of nine digits. How many Social Security numbers are possible that have the same first 6 digits

Accepted Answer

The answer of A Social Security number is a sequence...

Question 18

How many six-letter sequences are possible that use the letters g, o, b, l, i, n once each  ?

Accepted Answer

A) 216 
B)  120 
C)  720 
D)  6 
E)  36 
A) 216 
B)  120 
C)  720 
D)  6 
E)  36

Question 19

If $A = \{ \text { Klaas, Johan, Henrika, Sarie } \}$ and $C = \{ \text { Hans, Henrika } \}$ , then $n ( A \cup C ) = n ( A ) + n ( C ) - n ( A \cap C )$ .

Accepted Answer

A) True 
 B)False

Question 20

The "Dogs of the Dow" refer to the stocks listed on the Dow with the highest dividend yield. The table shows the top ten stocks of the "Dogs of the Dow" list in February, 2005. You decide to make a small portfolio consisting of a collection of seven of the top ten Dogs of the Dow. How many portfolios are possible  $$\begin{array} { | c | c | c | c | } 
\hline \text { Symbol } & \text { Company } & \text { Price } & \text { Yield } \
\hline \text { SBC } & \text { SBC } & 23.62 & 5.46 \% \
\hline \text { Communications } & \text { General Motors } & 36.64 & 5.46 \% \
\hline \text { MRK } & \text { Merck } & 28.02 & 5.42 \% \
\hline \text { MO } & \text { Altria } & 63.20 & 4.62 \% \
\hline \text { VZ } & \text { Verizon } & 35.68 & 4.32 \% \
\hline \text { JPM } & \text { JP Morgan Chase } & 37.00 & 3.68 \% \
\hline \text { C } & \text { Citigroup } & 48.38 & 3.64 \% \
\hline \text { PFE } & \text { Pfizer } & 24.35 & 3.12 \% \
\hline \text { DD } & \text { DuPont } & 47.23 & 2.96 \% \
\hline \text { GE } & \text { General Electric } & 35.75 & 2.46 \% \
\hline
\end{array}$$

Accepted Answer

A)  5,040 portfolios 
B)   21 portfolios 
C)   24 portfolios 
D)   120 portfolios 
E)   56 portfolios 
A)  5,040 portfolios 
B)   21 portfolios 
C)   24 portfolios 
D)   120 portfolios 
E)   56 portfolios

List the set of all outcomes of tossing three indistinguishable coins.

A telephone number consists of a sequence of seven digits not starting with a 0 or a 1. How many phone numbers begin with either 7,342, 7,423, or 7,224 ?

How many ordered sequences are possible that contain 2 objects chosen from 9

A test requires that you answer either Part A or Part B. Part A consists of 16 true-false questions and part B consists of 10 multiple-choice questions with one correct answer out of 3. How many different completed answer sheets are possible ?

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 3 lavender marbles. How many sets of 3 marbles include none of the yellow marbles

How many three-letter sequences are possible that contain only the letters R and D, with D occurring only once ?

In how many ways can a 5-card hand containing 4 kings and 1 queen be dealt from a deck of 52 cards

In a survey of 120 Enormous State University students, 22 enjoyed classical music, 24 enjoyed rock music, and 23 enjoyed house music. Only 6 of the students enjoyed both classical and rock. How many of those that enjoyed rock did not enjoy classical music ?

Given that $A = \{ \mathrm { H } , \mathrm { T } \}$ , and $B = \{ 1,2,3,4,5,6 \}$ , and $C = \{ \text { red, green, blue } \}$ . Find $n ( A \times B \times B )$ . $n ( A \times B \times B ) =$ __________

Given that $A = \{ \mathrm { H } , \mathrm { T } \}$ , $B = \{ 1,2,3,4,5 \}$ and $C = \{ \text { red, green, blue } \}$ . Find $n ( A \times B \times B )$ .

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 2 lavender marbles. How many sets of 4 marbles include at most one of the yellow marbles

Evaluate $\frac { 4 ! } { 1 ! }$ . $\frac { 4 ! } { 1 ! } =$ __________

A Social Security number is a sequence of nine digits. How many Social Security numbers are possible that have the same first 6 digits

How many six-letter sequences are possible that use the letters g, o, b, l, i, n once each ?

If $A = \{ \text { Klaas, Johan, Henrika, Sarie } \}$ and $C = \{ \text { Hans, Henrika } \}$ , then $n ( A \cup C ) = n ( A ) + n ( C ) - n ( A \cap C )$ .

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Exam 7: Sets and Counting

List the set of all outcomes of tossing three indistinguishable coins.

A telephone number consists of a sequence of seven digits not starting with a 0 or a 1. How many phone numbers begin with either 7,342, 7,423, or 7,224 ?

How many ordered sequences are possible that contain 2 objects chosen from 9

A test requires that you answer either Part A or Part B. Part A consists of 16 true-false questions and part B consists of 10 multiple-choice questions with one correct answer out of 3. How many different completed answer sheets are possible ?

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 3 lavender marbles. How many sets of 3 marbles include none of the yellow marbles

How many three-letter sequences are possible that contain only the letters R and D, with D occurring only once ?

In how many ways can a 5-card hand containing 4 kings and 1 queen be dealt from a deck of 52 cards

In a survey of 120 Enormous State University students, 22 enjoyed classical music, 24 enjoyed rock music, and 23 enjoyed house music. Only 6 of the students enjoyed both classical and rock. How many of those that enjoyed rock did not enjoy classical music ?

Given that A={H,T}A = \{ \mathrm { H } , \mathrm { T } \}A={H,T} , B={1,2,3,4,5}B = \{ 1,2,3,4,5 \}B={1,2,3,4,5} and C={ red, green, blue }C = \{ \text { red, green, blue } \}C={ red, green, blue } . Find n(A×B×B)n ( A \times B \times B )n(A×B×B) .

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 2 lavender marbles. How many sets of 4 marbles include at most one of the yellow marbles

Evaluate 4!1!\frac { 4 ! } { 1 ! }1!4!​ . ​ 4!1!=\frac { 4 ! } { 1 ! } =1!4!​= __________

A Social Security number is a sequence of nine digits. How many Social Security numbers are possible that have the same first 6 digits

How many six-letter sequences are possible that use the letters g, o, b, l, i, n once each ?

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Given that $A = \{ \mathrm { H } , \mathrm { T } \}$ , $B = \{ 1,2,3,4,5 \}$ and $C = \{ \text { red, green, blue } \}$ . Find $n ( A \times B \times B )$ .

Evaluate $\frac { 4 ! } { 1 ! }$ . $\frac { 4 ! } { 1 ! } =$ __________