Question 1

A surgical procedure requires four steps. The first step can result in 3 possible outcomes, the second in 5 possible outcomes, and the remaining two can each result in 4 possible outcomes. What is the total number of outcomes possible  ?

Accepted Answer

A) 300 
B)  240 
C)  16 
D)  60 
E)  180

Question 2

If $n ( A \cup B ) = 140$ and $n ( A ) = n ( B ) = 75$ , find $n ( A \cap B )$ .
​ $n ( A \cap B ) =$ __________

Accepted Answer

The answer of If \(n ( A \cup B )...

Question 3

Find the indicated value.
​
7!

Accepted Answer

The answer of Find the indicated value.
​
7!...

Question 4

Evaluate $C ( 3,1 )$ .
​ $C ( 3,1 ) =$ __________

Accepted Answer

The answer of Evaluate $C ( 3,1 )$ .
​ \(C...

Question 5

If $n ( A ) = 90$ , $n ( A \cup B ) = 190$ , and $n ( A \cap B ) = 30$ , find $n ( B )$ .
​ $n ( B ) =$ __________

Accepted Answer

The answer of If $n ( A ) = 90$...

Question 6

How many possible calendars are there that have February 15 falling on a Monday, or Tuesday  ?
__________ calendars

Accepted Answer

The answer of How many possible calendars are there that...

Question 7

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the flush (five cards all of the same suit, but not consecutive denominations: A, 2, 3, 4, 5 up through 10, J, Q, K, A). ​

Accepted Answer

A) 1,287 hands 
B)  5,108 hands 
C)  792 hands 
D)  5,148 hands 
E)  1,247 hands

Question 8

How many five-letter sequences are possible that use the letters b, l, a, c, k once each

Accepted Answer

The answer of How many five-letter sequences are possible that...

Question 9

In how many ways can a 6-card hand containing 4 kings and 2 queens be dealt from a deck of 36 cards

Accepted Answer

A) 1 
B)  288 
C)  576 
D)  6 
E)  4

Question 10

Evaluate   $C ( 7,4 )$ .

Accepted Answer

A)  840 
B)   6 
C)   24 
D)   210 
E)   35

Question 11

List the elements of all outcomes of rolling two indistinguishable dice such that the numbers add up to 8.
​
The answer is __________.

Accepted Answer

The answer of List the elements of all outcomes of...

Question 12

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 764, 768, or 788

Accepted Answer

The answer of A telephone number consists of a sequence...

Question 13

In an eight-cylinder engine, the even-numbered cylinders are on the left and the odd-numbered cylinders are on the right. A good firing order is a sequence of the numbers 1 through 8 in which right and left sides alternate. How many possible good firing sequences are there  ?

Accepted Answer

A) 40,320 sequences 
B)  512 sequences 
C)  576 sequences 
D)  1,152 sequences 
E)  24 sequences

Question 14

A test requires that you answer first Part A and then either Part B or Part C. Part A consists of 6 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  ?
__________ sheets

Accepted Answer

The answer of A test requires that you answer first...

Question 15

Let  $$\begin{aligned}
N & = \{ \text { small, medium, large } \} \
A & = \{ \text { hexagon, triangle } \}
\end{aligned}$$ 
List the elements of $N \times A$ as ordered pairs in a set notation.

Accepted Answer

A)  $\text { (small, hexagon) }$ , $\text { (medium, triangle) }$ , $\text { (large, triangle) }$ , $\text { (small, medium) }$ , $\text { (medium, large) }$ , $\text { (hexagon, triangle) }$ 
B)  $\text { (small, hexagon) }$ , $\text { (medium, hexagon) }$ , $\text { (large, hexagon) }$ , $\text { (small, triangle) }$ , $\text { (medium, triangle) }$ , $\text { (large, triangle) }$ 
C)  $\text { (small, hexagon) }$ , $\text { (medium, triangle) }$ , $\text { (small, large) }$ , $\text { (small, medium) }$ , $\text { (medium, large) }$ , $\text { (hexagon, triangle) }$ 
D)  $\text { (small, medium) }$ , $\text { (medium, large) }$ , $\text { (small, large) }$ , $\text { (hexagon, triangle) }$ 
E)  $\text { (small, hexagon) }$ , $\text { (medium, hexagon) }$ , $\text { (large, hexagon) }$ , $\text { (small, triangle) }$ , $\text { (medium, triangle) }$ , $\text { (hexagon, triangle) }$

Question 16

Evaluate $P ( 6,2 )$ .
​ $P ( 6,2 )$ __________

Accepted Answer

The answer of Evaluate $P ( 6,2 )$ .
​ \(P...

Question 17

The following table shows the amount spent, in billions of dollars, on recreational boats and accessories in the United States during the period 1999-2001. (Let S be the set of all dollars represented in the table.)
Compute the cardinality of the set described as $n ( N \cap C )$ . $$\begin{array} { | l | l | l | l | l | } 
\hline & \text { Used Boats, } \boldsymbol { U } & \text { New Boats, } \boldsymbol { N } & \text { Accessories, } \boldsymbol { R } & \text { Total } \
\hline \mathbf { 1 9 9 9 , } , \boldsymbol { A } & 5 & 6 & 3 & 14 \
\hline \mathbf { 2 0 0 0 } , \boldsymbol { B } & 9 & 9.5 & 4 & 22.5 \
\hline \mathbf { 2 0 0 1 } , \boldsymbol { C } & 9 & 6 & 4 & 19 \
\hline \text { Total } & 23 & 21.5 & 11 & 55.5 \
\hline
\end{array}$$ ​
​ $n ( N \cap C ) =$ __________ billion dollars.

Accepted Answer

The answer of The following table shows the amount spent,...

Question 18

Use the given information to complete the solution to the partially solved Venn diagram.   $$n ( A ) = 24$$ , $n ( B ) = 19$ , $n ( C ) = 30$ , $n ( A \cap C ) = 6$ , and $n ( S ) = 51$

Accepted Answer

A)    
B)     
C)     
D)     
E)

Question 19

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

Accepted Answer

A) 1 
B)  0 
C)  7 
D)  3 
E)  4

Question 20

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 1 lavender marble. How many possible sets of three marbles are ther

Accepted Answer

A)  220 
B)   1,320 
C)   6 
D)   720 
E)   440

Exam 7: Sets and Counting

A surgical procedure requires four steps. The first step can result in 3 possible outcomes, the second in 5 possible outcomes, and the remaining two can each result in 4 possible outcomes. What is the total number of outcomes possible ?

If $n ( A \cup B ) = 140$ and $n ( A ) = n ( B ) = 75$ , find $n ( A \cap B )$ . $n ( A \cap B ) =$ __________

Find the indicated value. 7!

Evaluate $C ( 3,1 )$ . $C ( 3,1 ) =$ __________

If $n ( A ) = 90$ , $n ( A \cup B ) = 190$ , and $n ( A \cap B ) = 30$ , find $n ( B )$ . $n ( B ) =$ __________

How many possible calendars are there that have February 15 falling on a Monday, or Tuesday ? __________ calendars

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the flush (five cards all of the same suit, but not consecutive denominations: A, 2, 3, 4, 5 up through 10, J, Q, K, A) .

How many five-letter sequences are possible that use the letters b, l, a, c, k once each

In how many ways can a 6-card hand containing 4 kings and 2 queens be dealt from a deck of 36 cards

Evaluate $C ( 7,4 )$ .

List the elements of all outcomes of rolling two indistinguishable dice such that the numbers add up to 8. The answer is __________.

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 764, 768, or 788

In an eight-cylinder engine, the even-numbered cylinders are on the left and the odd-numbered cylinders are on the right. A good firing order is a sequence of the numbers 1 through 8 in which right and left sides alternate. How many possible good firing sequences are there ?

Let $\begin{aligned}N & = \{ \text { small, medium, large } \} \\A & = \{ \text { hexagon, triangle } \}\end{aligned}$ List the elements of $N \times A$ as ordered pairs in a set notation.

Evaluate $P ( 6,2 )$ . $P ( 6,2 )$ __________

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 1 lavender marble. How many possible sets of three marbles are ther

Exam 7: Sets and Counting

A surgical procedure requires four steps. The first step can result in 3 possible outcomes, the second in 5 possible outcomes, and the remaining two can each result in 4 possible outcomes. What is the total number of outcomes possible ?

If n(A∪B)=140n ( A \cup B ) = 140n(A∪B)=140 and n(A)=n(B)=75n ( A ) = n ( B ) = 75n(A)=n(B)=75 , find n(A∩B)n ( A \cap B )n(A∩B) . ​ n(A∩B)=n ( A \cap B ) =n(A∩B)= __________

Find the indicated value. ​ 7!

Evaluate C(3,1)C ( 3,1 )C(3,1) . ​ C(3,1)=C ( 3,1 ) =C(3,1)= __________

If n(A)=90n ( A ) = 90n(A)=90 , n(A∪B)=190n ( A \cup B ) = 190n(A∪B)=190 , and n(A∩B)=30n ( A \cap B ) = 30n(A∩B)=30 , find n(B)n ( B )n(B) . ​ n(B)=n ( B ) =n(B)= __________

How many possible calendars are there that have February 15 falling on a Monday, or Tuesday ? __________ calendars

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the flush (five cards all of the same suit, but not consecutive denominations: A, 2, 3, 4, 5 up through 10, J, Q, K, A) . ​

How many five-letter sequences are possible that use the letters b, l, a, c, k once each

In how many ways can a 6-card hand containing 4 kings and 2 queens be dealt from a deck of 36 cards

Evaluate C(7,4) C ( 7,4 ) C(7,4) .

List the elements of all outcomes of rolling two indistinguishable dice such that the numbers add up to 8. ​ The answer is __________.

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 764, 768, or 788

In an eight-cylinder engine, the even-numbered cylinders are on the left and the odd-numbered cylinders are on the right. A good firing order is a sequence of the numbers 1 through 8 in which right and left sides alternate. How many possible good firing sequences are there ?

Let N={ small, medium, large }A={ hexagon, triangle }\begin{aligned}N & = \{ \text { small, medium, large } \} \\A & = \{ \text { hexagon, triangle } \}\end{aligned}NA​={ small, medium, large }={ hexagon, triangle }​ List the elements of N×AN \times AN×A as ordered pairs in a set notation.

Evaluate P(6,2)P ( 6,2 )P(6,2) . ​ P(6,2)P ( 6,2 )P(6,2) __________

Use the given information to complete the solution to the partially solved Venn diagram. n(A) =24n ( A ) = 24n(A) =24 , n(B) =19n ( B ) = 19n(B) =19 , n(C) =30n ( C ) = 30n(C) =30 , n(A∩C) =6n ( A \cap C ) = 6n(A∩C) =6 , and n(S) =51n ( S ) = 51n(S) =51

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 1 lavender marble. How many possible sets of three marbles are ther

If $n ( A \cup B ) = 140$ and $n ( A ) = n ( B ) = 75$ , find $n ( A \cap B )$ . $n ( A \cap B ) =$ __________

Find the indicated value. 7!

Evaluate $C ( 3,1 )$ . $C ( 3,1 ) =$ __________

If $n ( A ) = 90$ , $n ( A \cup B ) = 190$ , and $n ( A \cap B ) = 30$ , find $n ( B )$ . $n ( B ) =$ __________

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the flush (five cards all of the same suit, but not consecutive denominations: A, 2, 3, 4, 5 up through 10, J, Q, K, A) .

Evaluate $C ( 7,4 )$ .

List the elements of all outcomes of rolling two indistinguishable dice such that the numbers add up to 8. The answer is __________.

Let $\begin{aligned}N & = \{ \text { small, medium, large } \} \\A & = \{ \text { hexagon, triangle } \}\end{aligned}$ List the elements of $N \times A$ as ordered pairs in a set notation.

Evaluate $P ( 6,2 )$ . $P ( 6,2 )$ __________