Question 1

Use the information given in the figure.
- 
 How many are in B and C?

Accepted Answer

A)  1 
B)  37 
C)  3 
D)  47 
A)  1 
B)  37 
C)  3 
D)  47

Question 2

In a probability model, which of the following numbers could be the probability of an outcome: $0,0.2 , - 0.01 , - \frac { 1 } { 3 } , \frac { 1 } { 2 } , \frac { 5 } { 4 } , 1,1.5$

Accepted Answer

A)  $0.2 , \frac { 1 } { 2 } , 1$ 
B)  $0,0.2 , - 0.01,1,1$ 
C)  $0,0.2 , - 0.01 , - \frac { 1 } { 3 } , \frac { 1 } { 2 } , 1$ 
D)  $0,0.2 , \frac { 1 } { 2 } , 1$ 
A)  $0.2 , \frac { 1 } { 2 } , 1$ 
B)  $0,0.2 , - 0.01,1,1$ 
C)  $0,0.2 , - 0.01 , - \frac { 1 } { 3 } , \frac { 1 } { 2 } , 1$ 
D)  $0,0.2 , \frac { 1 } { 2 } , 1$

Question 3

Solve the problem.
-How many arrangements of answers are possible in a multiple-choice test with 7 questions, each of which has 3 possible answers?

Accepted Answer

A)  35 
B)  840 
C)  2187 
D)  210 
A)  35 
B)  840 
C)  2187 
D)  210

Question 4

Use the information given in the figure.
-  How many are not in C?

Accepted Answer

A)  39 
B)  45 
C)  36 
D)  40 
A)  39 
B)  45 
C)  36 
D)  40

Question 5

Solve the problem.
-How many 2-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can be used more than once.

Accepted Answer

A)  90 
B)  1,814,400 
C)  3,628,800 
D)  45 
A)  90 
B)  1,814,400 
C)  3,628,800 
D)  45

Question 6

Solve the problem.
-A group of 12 friends goes bowling. How many different possibilities are there for the order in which they play if the youngest person is to bowl first?

Accepted Answer

A)  39,916,800 
B)  479,001,600 
C)  12 
D)  11 
A)  39,916,800 
B)  479,001,600 
C)  12 
D)  11

Question 7

Solve the problem.
-A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false?

Accepted Answer

A)  1,048,576 
B)  190 
C)  40 
D)  400 
A)  1,048,576 
B)  190 
C)  40 
D)  400

Question 8

Solve the problem.
-How many different license plates can be made using 2 letters followed by 2 digits selected from the digits 0 through 9, if letters and digits may be repeated?

Accepted Answer

A)  260 
B)  67,600 
C)  4 
D)  36 
A)  260 
B)  67,600 
C)  4 
D)  36

Question 9

An environmental organization has 20 members. Each member will be placed on exactly 1 of 4 teams. Each team will work on a different issue. The first team has 5 members, the second has 4, the third has 8, and the
Fourth has 3. In how many ways can these teams be formed?

Accepted Answer

A)  2.432902008 × 1018 
B)  3.491888400 × 109 
C)  1.078721965 × 1016 
D)  1.047566520 × 1010 
A)  2.432902008 × 1018 
B)  3.491888400 × 109 
C)  1.078721965 × 1016 
D)  1.047566520 × 1010

Question 10

Solve the problem.
-How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 8 forwards, 10 midfield players, and 8 defensive players?

Accepted Answer

A)  322 
B)  568,995,840 
C)  658,560 
D)  5,311,735 
A)  322 
B)  568,995,840 
C)  658,560 
D)  5,311,735

Question 11

Write down all the subsets of the given set.
-$\{ 4 , \alpha , 9 , \pi \}$

Accepted Answer

A)  $\{ 4 \} , \{ \alpha \} , \{ 9 \} , \{ \pi \} , \{ 4 , \alpha \} , \{ 4,9 \} , \{ 4 , \pi \} , \{ \alpha , 9 \}$, $\{ \alpha , \pi \} , \{ 9 , \pi \} , \{ 4 , \alpha , 9 \} , \{ 4 , \alpha , \pi \} , \{ 4,9 , \pi \} , \{ \alpha , 9 , \pi \} , \varnothing$ 
B)  $\{ 4 \} , \{ \alpha \} , \{ 9 \} , \{ \pi \} , \{ 4 , \alpha \} , \{ 4,9 \} , \{ 4 , \pi \} , \{ \alpha , 9 \}$, $\{ \alpha , \pi \} , \{ 9 , \pi \} , \{ 4 , \alpha , \pi \} , \{ 4,9 , \pi \} , \{ \alpha , 9 , \pi \}$, $\{ 4 , \alpha , 9 , \pi \} , \varnothing$ 
C)  $\{ 4 \} , \{ \alpha \} , \{ 9 \} , \{ \pi \} , \{ 4 , \alpha \} , \{ 4,9 \} , \{ 4 , \pi \} , \{ \alpha , 9 \}$, $\{ \alpha , \pi \} , \{ 9 , \pi \} , \{ 4 , \alpha , 9 \} , \{ 4 , \alpha , \pi \} , \{ 4,9 , \pi \} , \{ \alpha , 9 , \pi \}$, $\{ 4 , \alpha , 9 , \pi \} , \varnothing$ 
D)  $\{ 4 \} , \{ \alpha \} , \{ 9 \} , \{ \pi \} , \{ 4 , \alpha \} , \{ 4,9 \} , \{ 4 , \pi \} , \{ \alpha , 9 \}$, $\{ \alpha , \pi \} , \{ 9 , \pi \} , \{ 4 , \alpha , 9 \} , \{ 4 , \alpha , \pi \} , \{ 4,9 , \pi \} , \{ \alpha , 9 , \pi \}$, $\{ 4 , \alpha , 9 , \pi \}$ 
A)  $\{ 4 \} , \{ \alpha \} , \{ 9 \} , \{ \pi \} , \{ 4 , \alpha \} , \{ 4,9 \} , \{ 4 , \pi \} , \{ \alpha , 9 \}$, $\{ \alpha , \pi \} , \{ 9 , \pi \} , \{ 4 , \alpha , 9 \} , \{ 4 , \alpha , \pi \} , \{ 4,9 , \pi \} , \{ \alpha , 9 , \pi \} , \varnothing$ 
B)  $\{ 4 \} , \{ \alpha \} , \{ 9 \} , \{ \pi \} , \{ 4 , \alpha \} , \{ 4,9 \} , \{ 4 , \pi \} , \{ \alpha , 9 \}$, $\{ \alpha , \pi \} , \{ 9 , \pi \} , \{ 4 , \alpha , \pi \} , \{ 4,9 , \pi \} , \{ \alpha , 9 , \pi \}$, $\{ 4 , \alpha , 9 , \pi \} , \varnothing$ 
C)  $\{ 4 \} , \{ \alpha \} , \{ 9 \} , \{ \pi \} , \{ 4 , \alpha \} , \{ 4,9 \} , \{ 4 , \pi \} , \{ \alpha , 9 \}$, $\{ \alpha , \pi \} , \{ 9 , \pi \} , \{ 4 , \alpha , 9 \} , \{ 4 , \alpha , \pi \} , \{ 4,9 , \pi \} , \{ \alpha , 9 , \pi \}$, $\{ 4 , \alpha , 9 , \pi \} , \varnothing$ 
D)  $\{ 4 \} , \{ \alpha \} , \{ 9 \} , \{ \pi \} , \{ 4 , \alpha \} , \{ 4,9 \} , \{ 4 , \pi \} , \{ \alpha , 9 \}$, $\{ \alpha , \pi \} , \{ 9 , \pi \} , \{ 4 , \alpha , 9 \} , \{ 4 , \alpha , \pi \} , \{ 4,9 , \pi \} , \{ \alpha , 9 , \pi \}$, $\{ 4 , \alpha , 9 , \pi \}$

Question 12

Find the value of the combination.
-C(10, 6)

Accepted Answer

A)  48 
B)  75,600 
C)  5040 
D)  210 
A)  48 
B)  75,600 
C)  5040 
D)  210

Question 13

Solve the problem.
-Lisa has 4 skirts, 9 blouses, and 3 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other?

Accepted Answer

A)  216 possible outfits 
B)  108 possible outfits 
C)  36 possible outfits 
D)  16 possible outfits 
A)  216 possible outfits 
B)  108 possible outfits 
C)  36 possible outfits 
D)  16 possible outfits

Question 14

Solve the problem.
-In how many ways can 6 people be lined up?

Accepted Answer

A)  1 
B)  6 
C)  360 
D)  720 
A)  1 
B)  6 
C)  360 
D)  720

Question 15

Solve the problem.
-How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0? Repeated digits are allowed.

Accepted Answer

A)  59,049 
B)  15,120 
C)  90,000 
D)  45,360 
A)  59,049 
B)  15,120 
C)  90,000 
D)  45,360

Question 16

Use the information given in the figure.
-  How many are in A or B or C?

Accepted Answer

A)  11 
B)  2 
C)  81 
D)  89 
A)  11 
B)  2 
C)  81 
D)  89

Question 17

Solve the problem.
-How many 6-symbol codes can be formed using 4 different symbols? Repeated symbols are allowed.

Accepted Answer

A)  15 
B)  30 
C)  360 
D)  4096 
A)  15 
B)  30 
C)  360 
D)  4096

Question 18

Solve the problem.
-List all the combinations of 4 objects 1, 2, 3, and 4 taken 3 at a time. What is C(4, 3)?

Accepted Answer

A)  $123,124,134,234,321,432$
$C ( 4,3 ) = 6$ 
B)  $123,124,134,234$
$C ( 4,3 ) = 4$ 
C)  $123,124,132,134,142,143,213,214,231,234,241,243,312,314,321,324,341,342,412,413,421,423,431$, 432
$C ( 4,3 ) = 24$ 
D)  $111,112,113,114,121,122,123,124,131,132,133,134,141,142,143,144,211,212,213,214,221,222,223$, $224,231,232,233,234,241,242,243,244,311,312,313,314,321,322,323,324,331,332,333,334,341,342$, $343,344,411,412,413,414,421,422,423,424,431,432,433,434,441,442,443,444$ 
$C ( 4,3 ) = 64$ 
A)  $123,124,134,234,321,432$
$C ( 4,3 ) = 6$ 
B)  $123,124,134,234$
$C ( 4,3 ) = 4$ 
C)  $123,124,132,134,142,143,213,214,231,234,241,243,312,314,321,324,341,342,412,413,421,423,431$, 432
$C ( 4,3 ) = 24$ 
D)  $111,112,113,114,121,122,123,124,131,132,133,134,141,142,143,144,211,212,213,214,221,222,223$, $224,231,232,233,234,241,242,243,244,311,312,313,314,321,322,323,324,331,332,333,334,341,342$, $343,344,411,412,413,414,421,422,423,424,431,432,433,434,441,442,443,444$ 
$C ( 4,3 ) = 64$

Question 19

Find the value of the combination.
-C(6, 6)

Accepted Answer

A)  180 
B)  1 
C)  720 
D)  0.5 
A)  180 
B)  1 
C)  720 
D)  0.5

Question 20

Solve the problem.
-Mary finds 10 fish at a pet store that she would like to buy, but she can afford only 4 of them. In how many ways can she make her selection? How many ways can she make her selection if he decides that one of the fish
Is a must?

Accepted Answer

A)  210; 84 
B)  151,200; 60,480 
C)  5040; 504 
D)  2520; 252 
A)  210; 84 
B)  151,200; 60,480 
C)  5040; 504 
D)  2520; 252

Use the information given in the figure. - How many are in B and C?

In a probability model, which of the following numbers could be the probability of an outcome: $0,0.2 , - 0.01 , - \frac { 1 } { 3 } , \frac { 1 } { 2 } , \frac { 5 } { 4 } , 1,1.5$

Solve the problem. -How many arrangements of answers are possible in a multiple-choice test with 7 questions, each of which has 3 possible answers?

Use the information given in the figure. - How many are not in C?

Solve the problem. -How many 2-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can be used more than once.

Solve the problem. -A group of 12 friends goes bowling. How many different possibilities are there for the order in which they play if the youngest person is to bowl first?

Solve the problem. -A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false?

Solve the problem. -How many different license plates can be made using 2 letters followed by 2 digits selected from the digits 0 through 9, if letters and digits may be repeated?

An environmental organization has 20 members. Each member will be placed on exactly 1 of 4 teams. Each team will work on a different issue. The first team has 5 members, the second has 4, the third has 8, and the Fourth has 3. In how many ways can these teams be formed?

Solve the problem. -How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 8 forwards, 10 midfield players, and 8 defensive players?

Write down all the subsets of the given set. - $\{ 4 , \alpha , 9 , \pi \}$

Find the value of the combination. -C(10, 6)

Solve the problem. -Lisa has 4 skirts, 9 blouses, and 3 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other?

Solve the problem. -In how many ways can 6 people be lined up?

Solve the problem. -How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0? Repeated digits are allowed.

Use the information given in the figure. - How many are in A or B or C?

Solve the problem. -How many 6-symbol codes can be formed using 4 different symbols? Repeated symbols are allowed.

Solve the problem. -List all the combinations of 4 objects 1, 2, 3, and 4 taken 3 at a time. What is C(4, 3)?

Find the value of the combination. -C(6, 6)

Solve the problem. -Mary finds 10 fish at a pet store that she would like to buy, but she can afford only 4 of them. In how many ways can she make her selection? How many ways can she make her selection if he decides that one of the fish Is a must?

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Filters

Exam 8: Counting and Probability

Use the information given in the figure. - How many are in B and C?

In a probability model, which of the following numbers could be the probability of an outcome: 0,0.2,−0.01,−13,12,54,1,1.50,0.2 , - 0.01 , - \frac { 1 } { 3 } , \frac { 1 } { 2 } , \frac { 5 } { 4 } , 1,1.50,0.2,−0.01,−31​,21​,45​,1,1.5

Solve the problem. -How many arrangements of answers are possible in a multiple-choice test with 7 questions, each of which has 3 possible answers?

Use the information given in the figure. - How many are not in C?

Solve the problem. -How many 2-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can be used more than once.

Solve the problem. -A group of 12 friends goes bowling. How many different possibilities are there for the order in which they play if the youngest person is to bowl first?

Solve the problem. -A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false?

Solve the problem. -How many different license plates can be made using 2 letters followed by 2 digits selected from the digits 0 through 9, if letters and digits may be repeated?

An environmental organization has 20 members. Each member will be placed on exactly 1 of 4 teams. Each team will work on a different issue. The first team has 5 members, the second has 4, the third has 8, and the Fourth has 3. In how many ways can these teams be formed?

Solve the problem. -How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 8 forwards, 10 midfield players, and 8 defensive players?

Write down all the subsets of the given set. - {4,α,9,π}\{ 4 , \alpha , 9 , \pi \}{4,α,9,π}

Find the value of the combination. -C(10, 6)

Solve the problem. -Lisa has 4 skirts, 9 blouses, and 3 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other?

Solve the problem. -In how many ways can 6 people be lined up?

Solve the problem. -How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0? Repeated digits are allowed.

Use the information given in the figure. - How many are in A or B or C?

Solve the problem. -How many 6-symbol codes can be formed using 4 different symbols? Repeated symbols are allowed.

Solve the problem. -List all the combinations of 4 objects 1, 2, 3, and 4 taken 3 at a time. What is C(4, 3)?

Find the value of the combination. -C(6, 6)

Solve the problem. -Mary finds 10 fish at a pet store that she would like to buy, but she can afford only 4 of them. In how many ways can she make her selection? How many ways can she make her selection if he decides that one of the fish Is a must?

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Filters

In a probability model, which of the following numbers could be the probability of an outcome: $0,0.2 , - 0.01 , - \frac { 1 } { 3 } , \frac { 1 } { 2 } , \frac { 5 } { 4 } , 1,1.5$

Write down all the subsets of the given set. - $\{ 4 , \alpha , 9 , \pi \}$