Question 1

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section.? ${ } _ { 5 } C _ { 2 }$ ?

Accepted Answer

A) 20 
B) 28 
C) 10 
D) 21 
E) 15 
A) 20 
B) 28 
C) 10 
D) 21 
E) 15

Question 2

Determine the number of ways a computer can randomly generate the integer that is divisible by 3 from 1 through 42.

Accepted Answer

A) 18 
B) 12 
C) 10 
D) 16 
E) 14 
A) 18 
B) 12 
C) 10 
D) 16 
E) 14

Question 3

A combination lock will open when the right choice of three numbers (from 1 to 35)is selected.How many different lock combinations are possible?

Accepted Answer

A) 1,225 
B) 42,875 
C) 128,625 
D) 35 
E) 105 
A) 1,225 
B) 42,875 
C) 128,625 
D) 35 
E) 105

Question 4

Determine the number of ways a computer can randomly generate the prime integers from 1 through 40. A prime integer

Accepted Answer

A) 10 
B) 14 
C) 12 
D) 8 
E) 16 
A) 10 
B) 14 
C) 12 
D) 8 
E) 16

Question 5

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 13 from 1 through 17 in increasing order. ​

Accepted Answer

A) 6 
B) 2 
C) 10 
D) 8 
E) 4 
A) 6 
B) 2 
C) 10 
D) 8 
E) 4

Question 6

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section.? ${ } _ { 48 } C _ { 5 }$ ?

Accepted Answer

A) 1,712,304 
B) 377,348,994 
C) 12,271,512 
D) 73,629,072 
E) 205,476,480 
A) 1,712,304 
B) 377,348,994 
C) 12,271,512 
D) 73,629,072 
E) 205,476,480

Question 7

Evaluate: ${ } _ { 15 } P _ { 5 }$

Accepted Answer

A) 32,760 
B) 75 
C) undefined 
D) 360,360 
E) 3,003 
A) 32,760 
B) 75 
C) undefined 
D) 360,360 
E) 3,003

Question 8

From a pool of 12 candidates,the offices of president,vice-president,secretary,and treasurer will be filled.In how many different ways can the offices be filled? ​

Accepted Answer

A) 12,380 
B) 13,380 
C) 12,880 
D) 13,880 
E) 11,880 
A) 12,380 
B) 13,380 
C) 12,880 
D) 13,880 
E) 11,880

Question 9

Determine the number of ways a computer can randomly generate the integers that is divisible by 4 from 1 through 40.

Accepted Answer

A) 14 
B) 12 
C) 10 
D) 6 
E) 8 
A) 14 
B) 12 
C) 10 
D) 6 
E) 8

Question 10

At a high school cafeteria,diners can choose one vegetable from a choice of 3 vegetables,one meat from a choice of 3 meats,one serving of bread from among 2 breads,and a dessert from among 2 desserts.How many meal configurations are possible?

Accepted Answer

A) 18 
B) 4 
C) 36 
D) 10 
E) 12 
A) 18 
B) 4 
C) 36 
D) 10 
E) 12

Question 11

In how many ways can a 22-question true-false exam be answered? (Assume that no questions are omitted. ) ​

Accepted Answer

A) 4,194,299 
B) 484 
C) 4,194,294 
D) 4,194,314 
E) ​4,194,304 
A) 4,194,299 
B) 484 
C) 4,194,294 
D) 4,194,314 
E) ​4,194,304

Question 12

​Evaluate the expression.​ $C ( 4,3 )$

Accepted Answer

The answer of ​Evaluate the expression.​ $C ( 4,3 )$...

Question 13

Evaluate ${ } _ { n } P _ { r }$ .? ${ } _ { 19 } P _ { 2 }$ ?

Accepted Answer

A) 420 
B) 380 
C) 342 
D) 462 
E) 171 
A) 420 
B) 380 
C) 342 
D) 462 
E) 171

Question 14

There are 15 patients in Dr.Ziglar's waiting room.Dr.Ziglar can see 6 patients before lunch.In how many different orders can Dr.Ziglar see 6 of the patients before lunch?

Accepted Answer

A) 90 
B) 6 
C) 1,816,214,400 
D) 3,603,600 
E) 5,005 
A) 90 
B) 6 
C) 1,816,214,400 
D) 3,603,600 
E) 5,005

Question 15

Evaluate ${ } _ { n } P _ { r }$ .? ${}_{40} P _ { 5 }$ ?

Accepted Answer

A) 2,193,360 
B) 658,008 
C) 59,280 
D) 78,960,960 
E) 2,763,633,600 
A) 2,193,360 
B) 658,008 
C) 59,280 
D) 78,960,960 
E) 2,763,633,600

Exam 57: Counting Principles

Evaluate nCr{ } _ { n } C _ { r }n​Cr​ using the formula from this section.? 5C2{ } _ { 5 } C _ { 2 }5​C2​ ?

Determine the number of ways a computer can randomly generate the integer that is divisible by 3 from 1 through 42.

A combination lock will open when the right choice of three numbers (from 1 to 35)is selected.How many different lock combinations are possible?

Determine the number of ways a computer can randomly generate the prime integers from 1 through 40. A prime integer

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 13 from 1 through 17 in increasing order. ​

Evaluate nCr{ } _ { n } C _ { r }n​Cr​ using the formula from this section.? 48C5{ } _ { 48 } C _ { 5 }48​C5​ ?

Evaluate: 15P5{ } _ { 15 } P _ { 5 }15​P5​

From a pool of 12 candidates,the offices of president,vice-president,secretary,and treasurer will be filled.In how many different ways can the offices be filled? ​

Determine the number of ways a computer can randomly generate the integers that is divisible by 4 from 1 through 40.

At a high school cafeteria,diners can choose one vegetable from a choice of 3 vegetables,one meat from a choice of 3 meats,one serving of bread from among 2 breads,and a dessert from among 2 desserts.How many meal configurations are possible?

In how many ways can a 22-question true-false exam be answered? (Assume that no questions are omitted. ) ​

​Evaluate the expression.​ C(4,3)C ( 4,3 )C(4,3)

Evaluate nPr{ } _ { n } P _ { r }n​Pr​ .? 19P2{ } _ { 19 } P _ { 2 }19​P2​ ?

There are 15 patients in Dr.Ziglar's waiting room.Dr.Ziglar can see 6 patients before lunch.In how many different orders can Dr.Ziglar see 6 of the patients before lunch?

Evaluate nPr{ } _ { n } P _ { r }n​Pr​ .? 40P5{}_{40} P _ { 5 }40​P5​ ?

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section.? ${ } _ { 5 } C _ { 2 }$ ?

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 13 from 1 through 17 in increasing order.

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section.? ${ } _ { 48 } C _ { 5 }$ ?

Evaluate: ${ } _ { 15 } P _ { 5 }$

From a pool of 12 candidates,the offices of president,vice-president,secretary,and treasurer will be filled.In how many different ways can the offices be filled?

In how many ways can a 22-question true-false exam be answered? (Assume that no questions are omitted. )

Evaluate the expression. $C ( 4,3 )$

Evaluate ${ } _ { n } P _ { r }$ .? ${ } _ { 19 } P _ { 2 }$ ?

Evaluate ${ } _ { n } P _ { r }$ .? ${}_{40} P _ { 5 }$ ?