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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

sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
Umesh Reply
I want to know trigonometry but I can't understand it anyone who can help
Siyabonga Reply
Yh
Idowu
which part of trig?
Nyemba
functions
Siyabonga
trigonometry
Ganapathi
differentiation doubhts
Ganapathi
hi
Ganapathi
hello
Brittany
Prove that 4sin50-3tan 50=1
Sudip Reply
f(x)= 1 x    f(x)=1x  is shifted down 4 units and to the right 3 units.
Sebit Reply
f (x) = −3x + 5 and g (x) = x − 5 /−3
Sebit
what are real numbers
Marty Reply
I want to know partial fraction Decomposition.
Adama Reply
classes of function in mathematics
Yazidu Reply
divide y2_8y2+5y2/y2
Sumanth Reply
wish i knew calculus to understand what's going on 🙂
Dashawn Reply
@dashawn ... in simple terms, a derivative is the tangent line of the function. which gives the rate of change at that instant. to calculate. given f(x)==ax^n. then f'(x)=n*ax^n-1 . hope that help.
Christopher
thanks bro
Dashawn
maybe when i start calculus in a few months i won't be that lost 😎
Dashawn
what's the derivative of 4x^6
Axmed Reply
24x^5
James
10x
Axmed
24X^5
Taieb
Thanks for this helpfull app
Axmed Reply
secA+tanA=2√5,sinA=?
richa Reply
tan2a+tan2a=√3
Rahulkumar
classes of function
Yazidu
if sinx°=sin@, then @ is - ?
NAVJIT Reply
the value of tan15°•tan20°•tan70°•tan75° -
NAVJIT
0.037 than find sin and tan?
Jon Reply
cos24/25 then find sin and tan
Deepak Reply
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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