PreCalculus 12 1 8.1 The Fundamental Counting Principle Olio’s Pizza sells 16 kinds of pizza, in 4 different sizes. If we initially select one kind of pizza, and then a size, we will find that there are: different possibilities of pizza and size. Example: A room has two dimming lights in it. If each light has 4 different settings, how many ways are there to set both lights? Example: how many 2 digit even whole numbers are there? Fundamental Counting Principle: If one task can be performed in _____ ways and a second can be performed in _____ ways, then the two tasks can be performed in _______ ways.
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PreCalculus 12
1
8.1TheFundamentalCountingPrinciple
Olio’sPizzasells16kindsofpizza,in4differentsizes.Ifweinitiallyselectonekindofpizza,andthenasize,
wewillfindthatthereare:
differentpossibilitiesofpizzaandsize.
Example:
Aroomhastwodimminglightsinit.Ifeachlighthas4differentsettings,howmanywaysaretheretosetboth
lights?
Example:howmany2digitevenwholenumbersarethere?
Fundamental Counting Principle:
If one task can be performed in _____ ways and a second can be performed in _____ ways, then the two tasks can be performed in _______ ways.
PreCalculus 12
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Example:IfBClicenseplateshavethepattern: LLL–NNN (whereL=letter,N=number)
Howmanylicenseplatesarepossible?
Howmanyarepossibleifletters&numberscannotberepeated?
OnyourOwn:Winnersishiring.Theirmanagerhasselectedfourpossibleapplicantsfortwodifferent
positionsatadepartmentstore.Inhowmanywayscanthemanagerfillthepositions?
a) usingthefundamentalcountingprinciple
b) usingatreediagram
Example:Justinisaterriblespeller,andfrequentlymisspellshisownname.
a) Ifheusesalltherightletters,howmanydifferentwayscanhemisspellhisname?
PreCalculus 12
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OnyourOwn:
b) Ifhehasthefirsttwoletterscorrect,howmanywayscanhestillmisspellhisname(assumingheuses
allthecorrectletters)?
Example:Inhowmanywayscanateacherseatfourgirlsandthreeboysinarowofsevenseatsifaboymust
beseatedateachendoftherow?
Themiddle5peoplecouldhavebeenseatedin_______________________arrangements.Thiscanbe
expressedas__________________,or________.
***Itisimportanttotakenoteofwhether___________________isallowedwhensolvingtheseproblems.
Ifnotthenwewillhavefar__________________options.***
Assignment:P.689#3-14MC1-3
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