Question 1

Evaluate the factorial expression.
-15 !

Accepted Answer

A)  $6.5385 \times 10 ^ { 11}$ 
B)  $8.7178 \times 10 ^ { 10}$ 
C)  $1.3077 \times 10 ^ { 12}$ 
D)  $2.6154 \times 10 ^ { 12 }$ 
A)  $6.5385 \times 10 ^ { 11}$ 
B)  $8.7178 \times 10 ^ { 10}$ 
C)  $1.3077 \times 10 ^ { 12}$ 
D)  $2.6154 \times 10 ^ { 12 }$

Question 2

Solve the problem.
-How many different committees can be selected from a group of 10 people if a committee must have between 2 and 4 people (inclusive)?

Accepted Answer

A) 420 
B) 276 
C) 375 
D) 326 
A) 420 
B) 276 
C) 375 
D) 326

Question 3

Evaluate the factorial expression.
-$\frac { 8 ! } { 6 ! 2 ! }$

Accepted Answer

A)  336 
B)  28 
C)  1 
D)  8 
A)  336 
B)  28 
C)  1 
D)  8

Question 4

Provide an appropriate response.
-Consider the selection of seven apples from a barrel of 75 apples. Is this a combination, a permutation, or neither?

Accepted Answer

A) Combination 
B) Permutation 
C) Neither 
A) Combination 
B) Permutation 
C) Neither

Question 5

Solve the problem.
-Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions with a large company. Find the number of different ways that five of these
People could be hired if the first two positions are to be filled by accounting majors, the third
Position is to be filled by an economics major, and the last two positions are to be filled by
Marketing majors.

Accepted Answer

A) 144 
B) 288 
C) 4 
D) 24 
A) 144 
B) 288 
C) 4 
D) 24

Question 6

Solve the problem.
-Given a group of 8 women and 11 men, how many different ways are there of choosing one man and one woman for a committee?

Accepted Answer

A) 361 
B) 19 
C) 88 
D) 342 
A) 361 
B) 19 
C) 88 
D) 342

Question 7

If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained?
-The sum of the two dice is at least 6.

Accepted Answer

A) 25 ways 
B) 6 ways 
C) 26 ways 
D) 21 ways 
A) 25 ways 
B) 6 ways 
C) 26 ways 
D) 21 ways

Question 8

Evaluate the expression.
-${ } _ { 32 } \mathrm { C } _ { 6 }$

Accepted Answer

A)  863,040 
B)  992 
C)  29,760 
D)  906,192 
A)  863,040 
B)  992 
C)  29,760 
D)  906,192

Question 9

Solve the problem.
-Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if Maria is to sit in the aisle seat?

Accepted Answer

A) 823,543 
B) 40, 320 
C) 5040 
D) 7 
A) 823,543 
B) 40, 320 
C) 5040 
D) 7

Question 10

Solve the problem.
-A baseball manager has 10 players of the same ability. How many different 9 player starting lineups can he create?

Accepted Answer

A) 362,880 
B) 3,628,800 
C) 10 
D) 90 
A) 362,880 
B) 3,628,800 
C) 10 
D) 90

Question 11

Solve the problem.
-A salesperson packed 3 shirts and 5 ties. With one shirt, he could wear all 5 ties. With another shirt, he could wear 4 ties. With the third shirt, he could wear only 2 ties. How many different Combinations did he have?

Accepted Answer

A) 40 combinations 
B) 11 combinations 
C) 10 combinations 
D) 22 combinations 
A) 40 combinations 
B) 11 combinations 
C) 10 combinations 
D) 22 combinations

Question 12

Evaluate the expression.
-${ } _ { 5 } C _ { 1 }$

Accepted Answer

A)  120 
B)  5 
C)  48 
D)  $2.5$ 
A)  120 
B)  5 
C)  48 
D)  $2.5$

Question 13

Solve the problem.
-If a license plate consists of four digits, how many different licenses could be created having at least one digit repeated.

Accepted Answer

A) 5040 licenses 
B) 4960 licenses 
C) 3024 licenses 
D) 10,000 licenses 
A) 5040 licenses 
B) 4960 licenses 
C) 3024 licenses 
D) 10,000 licenses

Question 14

Using the 36 possibilities found in the product table for rolling two dice, list and count the outcomes for which the sum (for both dice)is the following.
-Equal to 8

Accepted Answer

A) (2,6), (3,5), (4,4), (4,4), (5,3), (6,2); 6 
B) (2,6), (3,5); 2 
C) (2,6), (3,5), (4,4); 3 
D) (2,6), (3,5), (4,4), (5,3), (6,2); 5 
A) (2,6), (3,5), (4,4), (4,4), (5,3), (6,2); 6 
B) (2,6), (3,5); 2 
C) (2,6), (3,5), (4,4); 3 
D) (2,6), (3,5), (4,4), (5,3), (6,2); 5

Question 15

Provide an appropriate response.
-Consider the selection of a nominating committee for a club. Is this a combination, a permutation, or neither?

Accepted Answer

A) Permutation 
B) Combination 
C) Neither 
A) Permutation 
B) Combination 
C) Neither

Question 16

Solve the problem.
-How many two-digit counting numbers are either multiples of 2 or multiples of 3?

Accepted Answer

A) 75 numbers 
B) 15 numbers 
C) 60 numbers 
D) 61 numbers 
A) 75 numbers 
B) 15 numbers 
C) 60 numbers 
D) 61 numbers

Question 17

Evaluate the factorial expression.
-$\frac { 7 ! } { ( 7 - 4 ) ! }$

Accepted Answer

A)  7 
B)  210 
C)  1 
D)  840 
A)  7 
B)  210 
C)  1 
D)  840

Question 18

There are 13 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible?

Accepted Answer

A) 120 
B) 1287 
C) 154,440 
D) 371,293 
A) 120 
B) 1287 
C) 154,440 
D) 371,293

Question 19

Provide an appropriate response.
-Consider the selection of officers for a club. Is this a combination, a permutation, or neither?

Accepted Answer

A) Permutation 
B) Combination 
C) Neither 
A) Permutation 
B) Combination 
C) Neither

Question 20

Solve the problem.
-Of the 2,598,960 different five-card hands possible from a deck of 52 cards, how many contain at least one red card?

Accepted Answer

A) 2,598,959 hands 
B) 2,467,400 hands 
C) 1,266,590 hands 
D) 2,533,180 hands 
A) 2,598,959 hands 
B) 2,467,400 hands 
C) 1,266,590 hands 
D) 2,533,180 hands

Evaluate the factorial expression. -15 !

Solve the problem. -How many different committees can be selected from a group of 10 people if a committee must have between 2 and 4 people (inclusive)?

Evaluate the factorial expression. - $\frac { 8 ! } { 6 ! 2 ! }$

Provide an appropriate response. -Consider the selection of seven apples from a barrel of 75 apples. Is this a combination, a permutation, or neither?

Solve the problem. -Given a group of 8 women and 11 men, how many different ways are there of choosing one man and one woman for a committee?

If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? -The sum of the two dice is at least 6.

Evaluate the expression. - ${ } _ { 32 } \mathrm { C } _ { 6 }$

Solve the problem. -Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if Maria is to sit in the aisle seat?

Solve the problem. -A baseball manager has 10 players of the same ability. How many different 9 player starting lineups can he create?

Solve the problem. -A salesperson packed 3 shirts and 5 ties. With one shirt, he could wear all 5 ties. With another shirt, he could wear 4 ties. With the third shirt, he could wear only 2 ties. How many different Combinations did he have?

Evaluate the expression. - ${ } _ { 5 } C _ { 1 }$

Solve the problem. -If a license plate consists of four digits, how many different licenses could be created having at least one digit repeated.

Using the 36 possibilities found in the product table for rolling two dice, list and count the outcomes for which the sum (for both dice)is the following. -Equal to 8

Provide an appropriate response. -Consider the selection of a nominating committee for a club. Is this a combination, a permutation, or neither?

Solve the problem. -How many two-digit counting numbers are either multiples of 2 or multiples of 3?

Evaluate the factorial expression. - $\frac { 7 ! } { ( 7 - 4 ) ! }$

There are 13 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible?

Provide an appropriate response. -Consider the selection of officers for a club. Is this a combination, a permutation, or neither?

Solve the problem. -Of the 2,598,960 different five-card hands possible from a deck of 52 cards, how many contain at least one red card?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Exam 10: Counting Methods

Evaluate the factorial expression. -15 !

Solve the problem. -How many different committees can be selected from a group of 10 people if a committee must have between 2 and 4 people (inclusive)?

Evaluate the factorial expression. - 8!6!2!\frac { 8 ! } { 6 ! 2 ! }6!2!8!​

Provide an appropriate response. -Consider the selection of seven apples from a barrel of 75 apples. Is this a combination, a permutation, or neither?

Solve the problem. -Given a group of 8 women and 11 men, how many different ways are there of choosing one man and one woman for a committee?

If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? -The sum of the two dice is at least 6.

Evaluate the expression. - 32C6{ } _ { 32 } \mathrm { C } _ { 6 }32​C6​

Solve the problem. -Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if Maria is to sit in the aisle seat?

Solve the problem. -A baseball manager has 10 players of the same ability. How many different 9 player starting lineups can he create?

Solve the problem. -A salesperson packed 3 shirts and 5 ties. With one shirt, he could wear all 5 ties. With another shirt, he could wear 4 ties. With the third shirt, he could wear only 2 ties. How many different Combinations did he have?

Evaluate the expression. - 5C1{ } _ { 5 } C _ { 1 }5​C1​

Solve the problem. -If a license plate consists of four digits, how many different licenses could be created having at least one digit repeated.

Using the 36 possibilities found in the product table for rolling two dice, list and count the outcomes for which the sum (for both dice)is the following. -Equal to 8

Provide an appropriate response. -Consider the selection of a nominating committee for a club. Is this a combination, a permutation, or neither?

Solve the problem. -How many two-digit counting numbers are either multiples of 2 or multiples of 3?

Evaluate the factorial expression. - 7!(7−4)!\frac { 7 ! } { ( 7 - 4 ) ! }(7−4)!7!​

There are 13 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible?

Provide an appropriate response. -Consider the selection of officers for a club. Is this a combination, a permutation, or neither?

Solve the problem. -Of the 2,598,960 different five-card hands possible from a deck of 52 cards, how many contain at least one red card?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Evaluate the factorial expression. - $\frac { 8 ! } { 6 ! 2 ! }$

Evaluate the expression. - ${ } _ { 32 } \mathrm { C } _ { 6 }$

Evaluate the expression. - ${ } _ { 5 } C _ { 1 }$

Evaluate the factorial expression. - $\frac { 7 ! } { ( 7 - 4 ) ! }$