Powerpoint Counting Principle

7/25/2019 Powerpoint Counting Principle

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CountingCounting

OutcomesOutcomes


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Counting OutcomesCounting Outcomes

Have you ever seen or heard theHave you ever seen or heard theSubway or Starbucks advertisingSubway or Starbucks advertisingcampaigns where they talk about thecampaigns where they talk about the

10,000 different combinations of ways10,000 different combinations of waysto order a sub or drink?to order a sub or drink?


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Have you ever seen or heard theHave you ever seen or heard theSubway or Starbucks advertisingSubway or Starbucks advertisingcampaigns where they talk about thecampaigns where they talk about the

10,000 different combinations of ways10,000 different combinations of waysto order a sub or drink?to order a sub or drink?

hen companies like these makehen companies like these make

these claims they are using all thethese claims they are using all thedifferent condiments and ways todifferent condiments and ways toserve a drink!serve a drink!


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" #hese companies can use $%& ideas" #hese companies can use $%& ideasrelated to combinations to make theserelated to combinations to make theseclaims'claims'

$1& #()) *+-(.S$1& #()) *+-(.S

$%& #H) /*.)#2$%& #H) /*.)#2CO#+- 3(+C+32)CO#+- 3(+C+32)


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$1& #()) *+-(.S$1& #()) *+-(.S

tree diagram is a diagram used to show tree diagram is a diagram used to showthe total number of possible outcomes inthe total number of possible outcomes ina probability e4periment!a probability e4periment!


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$%& #H) /*.)#2$%& #H) /*.)#2CO#+- 3(+C+32)CO#+- 3(+C+32)

#he /undamental Counting 3rinciple uses#he /undamental Counting 3rinciple usesmultiplication of the number of ways eachmultiplication of the number of ways eachevent in an e4periment can occur to findevent in an e4periment can occur to findthe number of possible outcomes in athe number of possible outcomes in asample space!sample space!


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)4ample 1)4ample 1''#ree *iagrams!#ree *iagrams!

A new polo shirt is released in 4 differentA new polo shirt is released in 4 differentcolors and 5 different sizes. How manycolors and 5 different sizes. How many

different color and size combinationsdifferent color and size combinationsare available to the public?are available to the public?

Colors Colors (ed! "lue! #reen! $ellow%(ed! "lue! #reen! $ellow%

&tyles &tyles (&! '! ! )! ))%(&! '! ! )! ))%


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)4ample 1)4ample 1''#ree *iagrams!#ree *iagrams!

Answer.Answer.

eded "lue"lue #reen $ellow #reen $ellow

& ' ) ))& ' ) )) & ' ) )) & ' ) ))

& ' ) ))& ' ) )) & ' ) ))& ' ) ))

#here are#here are %0 different combinations%0 different combinations!!


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)4ample 1)4ample 1''#he /undamental Counting#he /undamental Counting3rinciple!3rinciple!

A new polo shirt is released in 4 differentA new polo shirt is released in 4 different

colors and 5 different sizes. How manycolors and 5 different sizes. How manydifferent color and size combinationsdifferent color and size combinationsare available to the public?are available to the public?

Colors Colors (ed! "lue! #reen! $ellow%(ed! "lue! #reen! $ellow%

&tyles &tyles (&! '! ! )! ))%(&! '! ! )! ))%


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Answer.Answer.

*umber of*umber of *umber of *umber of *umber of *umber of

+ossible &tyles+ossible &tyles +ossible &izes+ossible &izes +ossible Comb.+ossible Comb.

44 , , 55 - - //


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#ree *iagrams and #he /undamental#ree *iagrams and #he /undamentalCounting 3rinciple are two differentCounting 3rinciple are two differentalgorithms for finding sample space ofalgorithms for finding sample space of

a probability problem!a probability problem!

However, tree diagrams work betterHowever, tree diagrams work better

for some problems and thefor some problems and thefundamental counting principle worksfundamental counting principle worksbetter for other problems!better for other problems!


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)4ample %)4ample %''#ree *iagram!#ree *iagram!

0amara spins a spinner two0amara spins a spinner two

times. 1hat is her probabilitytimes. 1hat is her probability

of spinnin2 a 2reen on theof spinnin2 a 2reen on the

first spin and a blue on the second spin?first spin and a blue on the second spin?


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)4ample %)4ample %''#ree *iagram!#ree *iagram!

0amara spins a spinner two0amara spins a spinner two

times. 1hat is her probabilitytimes. 1hat is her probability

of spinnin2 a 2reen on theof spinnin2 a 2reen on the

first spin and a blue on the second spin?first spin and a blue on the second spin?

#reen#reen "lue "lue

#reen#reen "lue"lue #reen #reen "lue "lue

3nly one outcome has 2reen then blue! and there are 43nly one outcome has 2reen then blue! and there are 4possibilitiesso the +(2reen! blue% - or .5 or 56possibilitiesso the +(2reen! blue% - or .5 or 56


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7f a lottery 2ame is made up of three7f a lottery 2ame is made up of three

di2its from / to 8! what is thedi2its from / to 8! what is theprobability of winnin2 the 2ame?probability of winnin2 the 2ame?


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7f a lottery 2ame is made up of three di2its7f a lottery 2ame is made up of three di2its

from / to 8! what is the probability offrom / to 8! what is the probability ofwinnin2 if you buy 9 tic:et?winnin2 if you buy 9 tic:et?

; of +ossible; of +ossible ; of +ossible ; of +ossible ; of +ossible ; of +ossible ; of +ossible; of +ossible


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-uided 3ractice-uided 3ractice''*etermine the probability*etermine the probabilityfor each problem!for each problem!

(9% How many outfits are possible from a pair(9% How many outfits are possible from a pair

of >ean or :ha:i shorts and a choice ofof >ean or :ha:i shorts and a choice ofyellow! white! or blue shirt?yellow! white! or blue shirt?

(% &cott has 5 shirts! pairs of pants! and 4(% &cott has 5 shirts! pairs of pants! and 4pairs of soc:s. How many different outfitspairs of soc:s. How many different outfitscan &cott choose with a shirt! pair ofcan &cott choose with a shirt! pair of

pants! and pair of soc:s?pants! and pair of soc:s?


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-uided 3ractice-uided 3ractice''*etermine the probability*etermine the probabilityfor each problem!for each problem!

(9%(9% @ean &horts @ean &horts ha:i &hortsha:i &horts

$ellow$ellow 1hite "lue1hite "lue $ellow 1hite "lue$ellow 1hite "lue

@&$&@&$&99 @&1& @&1&.. @&"& @&"&?? &$&&$&44 &1& &1&55 &"& &"&BB

(% *umber(% *umber *umber*umber *umber*umber *umber*umber

3f &hirts3f &hirts 3f +ants3f +ants 3f &oc:s3f &oc:s 3f 3utfits3f 3utfits

6 4 5 4 7 86 4 5 4 7 8 9090


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(eal orld )4ample(eal orld )4ample''#he /undamental#he /undamentalCounting 3rinciple!Counting 3rinciple!

How many seven di2it telephone numbersHow many seven di2it telephone numbers

can be made up usin2 the di2its /8!can be made up usin2 the di2its /8!without repetition?without repetition?


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(eal orld )4ample(eal orld )4ample''#he /undamental#he /undamentalCounting 3rinciple!Counting 3rinciple!

How many seven di2it telephone numbersHow many seven di2it telephone numbers

can be made up usin2 the di2its /8!can be made up usin2 the di2its /8!without repetition?without repetition?

AnswerD B/4!E// different numbersAnswerD B/4!E// different numbers


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(eal orld )4ample(eal orld )4ample''#ree *iagram!#ree *iagram!

aitlyn tosses a coin times.


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(eal orld )4ample(eal orld )4ample''#ree *iagram!#ree *iagram!

aitlyn tosses a coin times.


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SummarySummary''

A A tree dia2ramtree dia2ramis used to show all of theis used to show all of thepossible outcomes! or sample space! in apossible outcomes! or sample space! in a

probability e,periment.probability e,periment. 0he 0he fundamental countin2 principlefundamental countin2 principle cancan

be used to count the number of possiblebe used to count the number of possible

outcomes 2iven an event that can happenoutcomes 2iven an event that can happenin some number of ways followed byin some number of ways followed byanother event that can happen in someanother event that can happen in some

number of different ways.number of different ways.


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SummarySummary''So when should + use a treeSo when should + use a treediagram or the fundamental countingdiagram or the fundamental countingprinciple?principle?

A A tree dia2ramtree dia2ramis used toDis used toD(9% show sample spaceG(9% show sample spaceG

(% count the number of preferred outcomes.(% count the number of preferred outcomes.

0he 0he fundamental countin2 principlefundamental countin2 principle cancanbe used toDbe used toD

(9% count the total number of outcomes.(9% count the total number of outcomes.

Powerpoint Counting Principle

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