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December 07, 2012

Nov 13­4:14 PM

UNIT 8

PERMUTATIONS AND COMBINATIONS

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http://www.google.ca/imgres?num=10&hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=tYjW7mLR_kf­8M:&imgrefurl=http://mathandmultimedia.com/tag/permutations­and­combinations/&docid=SVPQdfc5cSEePM&imgurl=http://mathandmultimedia.com/wp­content/uploads/2010/01/combinations1.png&w=353&h=240&ei=g9SiUJg3sc2KAti1gZAF&zoom=1&iact=rc&dur=557&sig=109971733282591085494&page=1&tbnh=132&tbnw=194&start=0&ndsp=25&ved=1t:429,r:8,s:0,i:92&tx=115&ty=104

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http://www.google.ca/imgres?hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=ZJt5zHySc00TiM:&imgrefurl=http://mrunal.org/2012/03/aptitude­pnc­arrange­such­that­two.html&docid=gbbtE_mKFPiA1M&imgurl=http://img706.imageshack.us/img706/7799/1alwayssittingtogether.png&w=551&h=324&ei=b9WiUKekAcaQiQKS7YDIAQ&zoom=1&iact=rc&dur=374&sig=109971733282591085494&page=1&tbnh=144&tbnw=245&start=0&ndsp=20&ved=1t:429,r:16,s:0,i:113&tx=131&ty=75

http://www.google.ca/imgres?hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=Ym7wbKUzcF1GbM:&imgrefurl=http://www.designsponge.com/2011/09/diy­project­vintage­style­book­dustcovers.html&docid=gw7QSE45jvySgM&imgurl=http://assets8.designsponge.com/wp­content/uploads/2011/09/dustcovers_intro.jpg&w=500&h=319&ei=3dWiUNfmFoaZiAL_54DoBQ&zoom=1&iact=rc&dur=446&sig=109971733282591085494&page=1&tbnh=134&tbnw=204&start=0&ndsp=24&ved=1t:429,r:1,s:0,i:68&tx=176&ty=69

Nov 13­4:22 PM

OUTCOMES:Permutations, Combinations and Binomial Theorem

It is expected that students will:

Develop algebraic and numeric reasoning that involves combinatorics. 

1. Apply the fundamental counting principle to solve problems.   2. Determine the number of permutations of n elements taken r at a time to solve problems.  3. Determine the number of combinations of n different elements taken rat a time to solve problems.  4. Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).    

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December 07, 2012

Nov 13­4:37 PM

LESSON 1

Fundamental Counting Principle

The students will apply the fundamental counting principle to solve problems

Dec 7­10:44 AM

Alberta has 3 different area codes for telephone numbers: 780, 403 and 587.  Even with three different area codes, within 5 years, Alberta will run out of assignable telephone numbers. 

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December 07, 2012

Nov 13­4:39 PM

INVESTIGATE

When solving problems involving many possibilities, there is need to organize a solution.  A tree diagram can be used to show all possibilities in an organized way.

1.From Vancouver, there are four routes to Calgary, two routesfrom Calgary to Brandon and two routes from Brandon to Saskatoon.  How many different routes are possible from Vancouver to Saskatoon.  (draw a tree diagram)

http://www.google.ca/imgres?num=10&hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=rREcdshnyMGwwM:&imgrefurl=http://www.qr77.com/News/Local/Story.aspx%3FID%3D1714632&docid=DuZU3AJ0IYd4yM&imgurl=http://www.qr77.com/Pics/_NEWS/June2012/calgary_tower.jpg&w=406&h=524&ei=IduiUKDKFqTviQLE04DYDg&zoom=1&iact=rc&dur=615&sig=109971733282591085494&sqi=2&page=1&tbnh=153&tbnw=115&start=0&ndsp=21&ved=1t:429,r:7,s:0,i:86&tx=89&ty=43

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http://www.google.ca/imgres?hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=3rZWEqbdgf­uhM:&imgrefurl=http://archiseek.com/2009/1901­brandon­college­brandon­manitoba/&docid=­kduRkAldDShEM&imgurl=http://archiseek.com/wp­content/gallery/canada­mb/brandon­university_lge.jpg&w=590&h=444&ei=lduiULCuE8WfiALb04GQAg&zoom=1&iact=rc&dur=343&sig=109971733282591085494&page=1&tbnh=138&tbnw=189&start=0&ndsp=22&ved=1t:429,r:5,s:0,i:80&tx=56&ty=91

http://www.google.ca/imgres?num=10&hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=yhvikNE2fSaFmM:&imgrefurl=http://www.usask.ca/cacsl2012/AboutSaskatoon&docid=cn4NRXfNi8aCMM&imgurl=http://www.usask.ca/stlhe2011/sites/default/files/images/744px­Saskatoon_Skyline_Night.jpg&w=744&h=600&ei=0tuiUN_FCbDpiwKhqYG4Ag&zoom=1&iact=hc&vpx=989&vpy=157&dur=320&hovh=202&hovw=250&tx=110&ty=117&sig=109971733282591085494&sqi=2&page=1&tbnh=157&tbnw=235&start=0&ndsp=15&ved=1t:429,r:4,s:0,i:77

Nov 13­4:48 PM

2.What are the possible outcomes for rolling a die and flippinga coin?  (draw a tree diagram)How many outcomes are there in total?

http://www.google.ca/imgres?hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=aap36uqK3bsocM:&imgrefurl=http://www.floodsite.net/juniorfloodsite/html/en/student/thingstoknow/geography/risk2.html&docid=0dqtJ7TigntLZM&imgurl=http://www.floodsite.net/juniorfloodsite/images/content/die.jpg&w=650&h=500&ei=mNyiULOkBYa­igKLkIGQDQ&zoom=1&iact=rc&dur=212&sig=109971733282591085494&page=1&tbnh=142&tbnw=185&start=0&ndsp=18&ved=1t:429,r:3,s:0,i:74&tx=123&ty=61

http://www.google.ca/imgres?hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=WcWtm3MVZAXiTM:&imgrefurl=http://theathletewithinyou.com/coin­flip­game­a­mental­game­exercise/&docid=lB4U9V8KT5mReM&imgurl=http://theathletewithinyou.com/wp­content/uploads/2012/10/coinflip.jpg&w=254&h=380&ei=xtyiULOmDoPiiAKm6YHYBg&zoom=1&iact=rc&dur=262&sig=109971733282591085494&page=1&tbnh=145&tbnw=99&start=0&ndsp=28&ved=1t:429,r:3,s:0,i:74&tx=19&ty=99

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December 07, 2012

Nov 13­4:51 PM

As the number of options become greater, it becomes more difficult to draw a tree diagram.

Look back at the last 2 examples.  Is there a way you could of found the overall amount of outcomes without doing a tree diagram?

Nov 13­4:53 PM

The Fundamental Counting Principle(FCP)

If a task is made up of stages, the total number of possibilies for the taskis given by m x n x p x ...., where m is the number of choices for the firststage, n is the number of choices for the second stage, p is the number of choices for the third stage, etc.

http://www.google.ca/imgres?num=10&hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=spnNorTEvrh0RM:&imgrefurl=http://www.christart.com/clipart/image/yippee_0f4&docid=t5GN9RMp3173EM&imgurl=http://www.christart.com/IMAGES­art9ab/clipart/2560/0f4/yippee.png&w=300&h=300&ei=It6iUNXyBsSeiQLz_oHQAQ&zoom=1&iact=rc&dur=256&sig=109971733282591085494&sqi=2&page=1&tbnh=139&tbnw=139&start=0&ndsp=27&ved=1t:429,r:6,s:0,i:83&tx=71&ty=86

Does FCP work on the last 2 examples?

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December 07, 2012

Nov 14­11:25 AM

EXAMPLES:1.  The assembly of a new automobile requires that certain choicesbe made.  For example, what color, what type of transmission, type of interior, air­conditioning or not.  Given the following tableof options, in how many different ways can this automobile beassembled?

COLOR TRANSMISSION

TYPE OFINTERIOR

AIR CONDITIONING

Red Automatic Cloth Yes

Black Standard Leather No

Silver

White

https://www.google.ca/search?num=10&hl=en&authuser=0&site=imghp&tbm=isch&source=hp&biw=1280&bih=675&q=gmc+acadia&oq=gmc+acadia&gs_l=img.3..0l10.10250.12572.0.12699.14.10.1.3.3.0.162.958.6j4.10.0...0.0...1ac.1.OyONqfmGiks&safe=active

Nov 14­11:47 AM

2.How many different license plates can be made that consist of three 

letters followed by three digits?

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December 07, 2012

Nov 14­11:50 AM

3. If a person has 4 different pairs of pants and 7 different shirts.  How many ways 

is there to make an outfit?

https://www.google.ca/search?num=10&hl=en&authuser=0&site=imghp&tbm=isch&source=hp&biw=1280&bih=675&q=gmc+acadia&oq=gmc+acadia&gs_l=img.3..0l10.10250.12572.0.12699.14.10.1.3.3.0.162.958.6j4.10.0...0.0...1ac.1.OyONqfmGiks&safe=active#hl=en&safe=active&authuser=0&site=imghp&tbm=isch&sa=1&q=+pants&oq=+pants&gs_l=img.3..0l10.6875.6875.2.7950.1.1.0.0.0.0.392.392.3­1.1.0...0.0...1c.1.TWiM1475BJQ&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&fp=264a54fb63ff38ea&bpcl=38626820&biw=1280&bih=675

http://www.google.ca/imgres?start=157&hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=_NzrM­LfwjQ2BM:&imgrefurl=http://www.typotheque.com/tshirts/colour_of_the_day&docid=Il05YirSuPmIFM&imgurl=http://im.typotheque.com/tshirts/gallery/7shirts.jpg&w=738&h=459&ei=I­mjUPDrHYS0qQHP2IGoDg&zoom=1&iact=hc&vpx=332&vpy=387&dur=3429&hovh=177&hovw=285&tx=164&ty=80&sig=109971733282591085494&page=7&tbnh=135&tbnw=213&ndsp=30&ved=1t:429,r:76,s:100,i:232

Nov 14­11:57 AM

4. If the same person from the last question also has 5 pairs of shoes.  How 

many outfits that can be made?

https://www.google.ca/search?num=10&hl=en&authuser=0&site=imghp&tbm=isch&source=hp&biw=1280&bih=675&q=gmc+acadia&oq=gmc+acadia&gs_l=img.3..0l10.10250.12572.0.12699.14.10.1.3.3.0.162.958.6j4.10.0...0.0...1ac.1.OyONqfmGiks&safe=active#hl=en&safe=active&authuser=0&site=imghp&tbm=isch&sa=1&q=sport+chek+shoes&oq=sport+chek+shoes&gs_l=img.3...16867.20940.2.21111.17.15.2.0.0.6.964.3733.0j3j6j6­2.11.0...0.0...1c.1.Y6WvwYi3ZKI&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&fp=264a54fb63ff38ea&bpcl=38626820&biw=1280&bih=675

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December 07, 2012

Nov 14­12:02 PM

5.A restaurant offers 6 different entrees, with a choice of 3 different types of potatoes, 3 different types of salads, and 5 different beverages.  How many different lunches can be ordered?

http://www.google.ca/imgres?num=10&hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=J7KtVoEMXp9UdM:&imgrefurl=http://www.saharaonline.ca/lunch%2520buffet.html&docid=D7nnHIocJZBGKM&imgurl=http://www.saharaonline.ca/images/PIC­buffet­2.jpg&w=228&h=399&ei=TOujULuMGMqPqgGkmoH4BA&zoom=1&iact=rc&dur=309&sig=109971733282591085494&sqi=2&page=1&tbnh=144&tbnw=80&start=0&ndsp=17&ved=1t:429,r:6,s:0,i:83&tx=42&ty=73

Nov 14­12:06 PM

6.The final score in a hockey game is  5 – 2.  How many different scores 

are possible at the end of the second period?

5 2

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December 07, 2012

Nov 14­12:10 PM

FUNDAMENTAL COUNTING PRINCIPLE WITH RESTRICTIONS

7.a)Write all 2 digit odd numbers that can be made using the digits 0,1,2,3,4,5

b)Solve the following problem using the fundamental counting principle.How many 2 digit odd numbers that can be made using the digits 0,1,2,3,4,5?

Nov 14­12:12 PM

8.The dial on a 3­number combination lock contains markings to represent 

the numbers 0 to 59.  How many different combinations are possible if no 

two numbers are the same.

http://www.google.ca/imgres?num=10&hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=O2auCFpcl_5ZzM:&imgrefurl=http://dualcrown.en.made­in­china.com/product/FMNEvIzJEghB/China­Combination­Lock­5250­.html&docid=wT9tY0c3l5x99M&imgurl=http://image.made­in­china.com/2f0j00mMNEsVDarHbj/Combination­Lock­5250­.jpg&w=600&h=600&ei=W­2jUMO0Asv­2QXiyoCoCw&zoom=1&iact=rc&dur=266&sig=109971733282591085494&page=1&tbnh=147&tbnw=149&start=0&ndsp=27&ved=1t:429,r:0,s:0,i:68&tx=87&ty=40

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December 07, 2012

Nov 14­12:14 PM

9.Determine the number of distinguishable four letter arrangements that can be 

formed from the word ENGLISH no letters are repeated and:

i) there are no further restrictions?ii) the first letter must be E?

iii) the “word” must contain G?iv)  the first and last letters must be vowels?

Nov 14­12:15 PM

U8 L1 Assignment