Question 1

?Evaluate the expression.? $P ( 8,5 )$ ?

Accepted Answer

A) ?48 
B) ?6 
C) ?6,720 
D) ?80,640 
E) ?none of the above 
A) ?48 
B) ?6 
C) ?6,720 
D) ?80,640 
E) ?none of the above

Question 2

Find the number of distinguishable permutations of the group of letters. G,A,U,S,S

Accepted Answer

A) ​15 
B) ​5 
C) ​120 
D) ​60 
E) ​30 
A) ​15 
B) ​5 
C) ​120 
D) ​60 
E) ​30

Question 3

Evaluate ${ } _ { n } P _ { r }$ .? ${ } _ { 16 } P _ { 8 }$ ?

Accepted Answer

A) 57,657,600 
B) 524,160 
C) 5,765,760 
D) 518,918,400 
E) 12,870 
A) 57,657,600 
B) 524,160 
C) 5,765,760 
D) 518,918,400 
E) 12,870

Question 4

Solve for n.? $56 ^ { . }~ {}_{ n - 1} P _ { 6 } = { } _ { n + 1 } P _ { 7 }$

Accepted Answer

A) no solution 
B) ?n = 7 
C) ?n = 7,48 
D) ?n = 8,47 
E) ?n = 48 
A) no solution 
B) ?n = 7 
C) ?n = 7,48 
D) ?n = 8,47 
E) ?n = 48

Question 5

How many four-digit numbers can be formed under the following condition? ​
The leading digit cannot be zero and the number must be less than 7,000.
​

Accepted Answer

A) 5,800 
B) 6,000 
C) 5,700 
D) 5,600 
E) 5,900 
A) 5,800 
B) 6,000 
C) 5,700 
D) 5,600 
E) 5,900

Question 6

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

Accepted Answer

A) 138 
B) 128 
C) 133 
D) 118 
E) 123 
A) 138 
B) 128 
C) 133 
D) 118 
E) 123

Question 7

How many three-digit numbers can be formed under the following condition? ​
The number is at least 400.
​

Accepted Answer

A) 590 
B) 610 
C) 620 
D) 580 
E) 600 
A) 590 
B) 610 
C) 620 
D) 580 
E) 600

Question 8

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 20 from 1 through 25 in increasing order. ​

Accepted Answer

A) 7 
B) 5 
C) 11 
D) 13 
E) 9 
A) 7 
B) 5 
C) 11 
D) 13 
E) 9

Question 9

Which scenario(s)below should be counted using permutations? I.the number of ways the gold,silver,and bronze medal winners can be chosen in an Olympic track-and-field event (assume that there are no ties)
II.the number of ways 3 people can be chosen to sit from among 8 people
III.the number of ways to choose 5 lottery numbers
IV.the number of ways to roll a total of 7 when rolling a pair of dice
V.the permutation may not be used in any scenarios

Accepted Answer

A) ​II only 
B) ​I only 
C) ​V only 
D) ​IV only 
E) ​III only 
A) ​II only 
B) ​I only 
C) ​V only 
D) ​IV only 
E) ​III only

Question 10

Evaluate the expression.​​ $P ( 9,9 )$

Accepted Answer

The answer of Evaluate the expression.​​ $P ( 9,9 )$...

Question 11

Evaluate ${ } _ { n } P _ { r }$ .? $${ } _ { 7 } P _ { 3 }$$ ?

Accepted Answer

A) 210 
B) 336 
C) 720 
D) 35 
E) 504 
A) 210 
B) 336 
C) 720 
D) 35 
E) 504

Question 12

Evaluate using a graphing utility: ${ } _ { 15 } P _ { 5 }$

Accepted Answer

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

Question 13

In how many ways can seven people sit in a seven-passenger car? ​

Accepted Answer

A) 6,040 
B) 5,090 
C) 5,040 
D) 5,140 
E) 5,540 
A) 6,040 
B) 5,090 
C) 5,040 
D) 5,140 
E) 5,540

Question 14

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section.? ${ } _ { 11 } C _ { 0 }$ ?

Accepted Answer

A) 11 
B) 1 
C) 55 
D) 165 
E) 330 
A) 11 
B) 1 
C) 55 
D) 165 
E) 330

Question 15

Determine the number of ways a computer can randomly generate the odd integers from 1 through 26. ​

Accepted Answer

A) 11 
B) 15 
C) 17 
D) 13 
E) 9 
A) 11 
B) 15 
C) 17 
D) 13 
E) 9

Question 16

Evaluate ${ } _ { n } P _ { r }$ .? ${}_{100} P _ { 5 }$ ?

Accepted Answer

A) 94,109,400 
B) 970,200 
C) 75,287,520 
D) 9,034,502,400 
E) 858,277,728,000 
A) 94,109,400 
B) 970,200 
C) 75,287,520 
D) 9,034,502,400 
E) 858,277,728,000

Question 17

Determine the number of ways a computer can randomly generate the integers that is greater than 8 from 1 through 12.

Accepted Answer

A) 8 
B) 6 
C) 0 
D) 4 
E) 2 
A) 8 
B) 6 
C) 0 
D) 4 
E) 2

Question 18

How many 3-digit numbers can be formed if the leading digit cannot be zero?

Accepted Answer

A) ​900 
B) 100 
C) 9999 
D) 901 
E) 999 
A) ​900 
B) 100 
C) 9999 
D) 901 
E) 999

Question 19

A baseball coach is creating a nine-player batting order by selecting from a team of 19 players.How many different batting orders are possible? ​

Accepted Answer

A) 33,522,128,640 
B) 33,523,128,640 
C) 33,522,628,640 
D) 33,572,128,640 
E) 33,532,128,640 
A) 33,522,128,640 
B) 33,523,128,640 
C) 33,522,628,640 
D) 33,572,128,640 
E) 33,532,128,640

Question 20

?Evaluate the expression.? $C ( 5,2 )$ ?

Accepted Answer

A) ?60 
B) ?120 
C) ?2 
D) ?20 
E) ?10 
A) ?60 
B) ?120 
C) ?2 
D) ?20 
E) ?10

Exam 57: Counting Principles

?Evaluate the expression.? P(8,5)P ( 8,5 )P(8,5) ?

Find the number of distinguishable permutations of the group of letters. G,A,U,S,S

Evaluate nPr{ } _ { n } P _ { r }n​Pr​ .? 16P8{ } _ { 16 } P _ { 8 }16​P8​ ?

Solve for n.? 56. n−1P6=n+1P756 ^ { . }~ {}_{ n - 1} P _ { 6 } = { } _ { n + 1 } P _ { 7 }56. n−1​P6​=n+1​P7​

How many four-digit numbers can be formed under the following condition? ​ The leading digit cannot be zero and the number must be less than 7,000. ​

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

How many three-digit numbers can be formed under the following condition? ​ The number is at least 400. ​

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 20 from 1 through 25 in increasing order. ​

Evaluate the expression.​​ P(9,9)P ( 9,9 )P(9,9)

Evaluate nPr{ } _ { n } P _ { r }n​Pr​ .? 7P3{ } _ { 7 } P _ { 3 }7​P3​ ?

Evaluate using a graphing utility: 15P5{ } _ { 15 } P _ { 5 }15​P5​

In how many ways can seven people sit in a seven-passenger car? ​

Evaluate nCr{ } _ { n } C _ { r }n​Cr​ using the formula from this section.? 11C0{ } _ { 11 } C _ { 0 }11​C0​ ?

Determine the number of ways a computer can randomly generate the odd integers from 1 through 26. ​

Evaluate nPr{ } _ { n } P _ { r }n​Pr​ .? 100P5{}_{100} P _ { 5 }100​P5​ ?

Determine the number of ways a computer can randomly generate the integers that is greater than 8 from 1 through 12.

How many 3-digit numbers can be formed if the leading digit cannot be zero?

A baseball coach is creating a nine-player batting order by selecting from a team of 19 players.How many different batting orders are possible? ​

?Evaluate the expression.? C(5,2)C ( 5,2 )C(5,2) ?

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

?Evaluate the expression.? $P ( 8,5 )$ ?

Evaluate ${ } _ { n } P _ { r }$ .? ${ } _ { 16 } P _ { 8 }$ ?

Solve for n.? $56 ^ { . }~ {}_{ n - 1} P _ { 6 } = { } _ { n + 1 } P _ { 7 }$

How many four-digit numbers can be formed under the following condition? The leading digit cannot be zero and the number must be less than 7,000.

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

How many three-digit numbers can be formed under the following condition? The number is at least 400.

Determine the number of ways a computer can randomly generate two distinct integers whose sum is 20 from 1 through 25 in increasing order.

Evaluate the expression. $P ( 9,9 )$

Evaluate ${ } _ { n } P _ { r }$ .? ${ } _ { 7 } P _ { 3 }$ ?

Evaluate using a graphing utility: ${ } _ { 15 } P _ { 5 }$

In how many ways can seven people sit in a seven-passenger car?

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section.? ${ } _ { 11 } C _ { 0 }$ ?

Determine the number of ways a computer can randomly generate the odd integers from 1 through 26.

Evaluate ${ } _ { n } P _ { r }$ .? ${}_{100} P _ { 5 }$ ?

A baseball coach is creating a nine-player batting order by selecting from a team of 19 players.How many different batting orders are possible?

?Evaluate the expression.? $C ( 5,2 )$ ?