PreCalculus 12

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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.

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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?

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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