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Section exercises

Verbal

For the following exercises, assume that there are n ways an event A can happen, m ways an event B can happen, and that A  and  B are non-overlapping.

Use the Addition Principle of counting to explain how many ways event A  or  B can occur.

There are m + n ways for either event A or event B to occur.

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Use the Multiplication Principle of counting to explain how many ways event A  and  B can occur.

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Answer the following questions.

When given two separate events, how do we know whether to apply the Addition Principle or the Multiplication Principle when calculating possible outcomes? What conjunctions may help to determine which operations to use?

The addition principle is applied when determining the total possible of outcomes of either event occurring. The multiplication principle is applied when determining the total possible outcomes of both events occurring. The word “or” usually implies an addition problem. The word “and” usually implies a multiplication problem.

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Describe how the permutation of n objects differs from the permutation of choosing r objects from a set of n objects. Include how each is calculated.

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What is the term for the arrangement that selects r objects from a set of n objects when the order of the r objects is not important? What is the formula for calculating the number of possible outcomes for this type of arrangement?

A combination; C ( n , r ) = n ! ( n r ) ! r !

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Numeric

For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.

Let the set A = { 5 , 3 , 1 , 2 , 3 , 4 , 5 , 6 } . How many ways are there to choose a negative or an even number from A?

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Let the set B = { 23 , 16 , 7 , 2 , 20 , 36 , 48 , 72 } . How many ways are there to choose a positive or an odd number from A ?

4 + 2 = 6

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How many ways are there to pick a red ace or a club from a standard card playing deck?

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How many ways are there to pick a paint color from 5 shades of green, 4 shades of blue, or 7 shades of yellow?

5 + 4 + 7 = 16

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How many outcomes are possible from tossing a pair of coins?

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How many outcomes are possible from tossing a coin and rolling a 6-sided die?

2 × 6 = 12

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How many two-letter strings—the first letter from A and the second letter from B can be formed from the sets A = { b , c , d } and B = { a , e , i , o , u } ?

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How many ways are there to construct a string of 3 digits if numbers can be repeated?

10 3 = 1000

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How many ways are there to construct a string of 3 digits if numbers cannot be repeated?

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For the following exercises, compute the value of the expression.

P ( 5 , 2 )

P ( 5 , 2 ) = 20

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P ( 3 , 3 )

P ( 3 , 3 ) = 6

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P ( 11 , 5 )

P ( 11 , 5 ) = 55 , 440

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C ( 12 , 4 )

C ( 12 , 4 ) = 495

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C ( 7 , 6 )

C ( 7 , 6 ) = 7

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For the following exercises, find the number of subsets in each given set.

{ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }

2 10 = 1024

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{ a , b , c , , z }

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A set containing 5 distinct numbers, 4 distinct letters, and 3 distinct symbols

2 12 = 4096

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The set of even numbers from 2 to 28

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The set of two-digit numbers between 1 and 100 containing the digit 0

2 9 = 512

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For the following exercises, find the distinct number of arrangements.

Questions & Answers

how do I set up the problem?
Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
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Shirley Reply
please can go further on polynomials quadratic
Abdullahi
I need quadratic equation link to Alpa Beta
Abdullahi Reply
find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
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Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
Practice Key Terms 5

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Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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