8.1 The Fundamental Counting Principle · 8.1 The Fundamental Counting Principle Olio’s Pizza...
Transcript of 8.1 The Fundamental Counting Principle · 8.1 The Fundamental Counting Principle Olio’s Pizza...
![Page 1: 8.1 The Fundamental Counting Principle · 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,](https://reader030.fdocuments.net/reader030/viewer/2022040621/5f374d42e55e492aab5feeba/html5/thumbnails/1.jpg)
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.
![Page 2: 8.1 The Fundamental Counting Principle · 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,](https://reader030.fdocuments.net/reader030/viewer/2022040621/5f374d42e55e492aab5feeba/html5/thumbnails/2.jpg)
PreCalculus 12
2
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?
![Page 3: 8.1 The Fundamental Counting Principle · 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,](https://reader030.fdocuments.net/reader030/viewer/2022040621/5f374d42e55e492aab5feeba/html5/thumbnails/3.jpg)
PreCalculus 12
3
OnyourOwn:
b) Ifhehasthefirsttwoletterscorrect,howmanywayscanhestillmisspellhisname(assumingheuses
allthecorrectletters)?
Example:Inhowmanywayscanateacherseatfourgirlsandthreeboysinarowofsevenseatsifaboymust
beseatedateachendoftherow?
Themiddle5peoplecouldhavebeenseatedin_______________________arrangements.Thiscanbe
expressedas__________________,or________.
***Itisimportanttotakenoteofwhether___________________isallowedwhensolvingtheseproblems.
Ifnotthenwewillhavefar__________________options.***
Assignment:P.689#3-14MC1-3