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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

the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
what is cell divisoin?
Aron Reply
Diversity of living thing
ISCONT
what is cell division
Aron Reply
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
What is life?
Allison Reply
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
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Practice Key Terms 5

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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