Math 30­1 day 2 Permutations and Factorial Notation notes.notebook

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September 07, 2016

Nov 15­11:56 AM

LESSON 2Factorial Notation

Factorial Notation:

The product of consecutive natural numbers, in decreasing order to the number one, can be represented using factorial notation.

5! = 5 x 4 x 3 x 2 x 1 = 120

4! =                                         =

8! =                                                       =

Can you find a "!" button on your calculator?  If so, try it!

Nov 15­12:03 PM

In general terms:

n! =  

Math 30­1 day 2 Permutations and Factorial Notation notes.notebook

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September 07, 2016

Nov 15­12:06 PM

Evaluate:Using the factorial key on your calculator to evaluate:

a)                                          b)                                           c)

d)                                          e)

Nov 15­12:12 PM

EXAMPLES:

1.Solve by cancellation.

a) b)

c) d)

Math 30­1 day 2 Permutations and Factorial Notation notes.notebook

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September 07, 2016

Nov 15­12:17 PM

2.Simplify the following expressions

a) b)

c) d)

Nov 15­3:02 PM

3.Find the value of the following.  

i)a)                                                                      b)

ii)a)                                                                    b)

iii)a)

iv)a)b)

Math 30­1 day 2 Permutations and Factorial Notation notes.notebook

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September 07, 2016

Nov 15­3:22 PM

4.Solve each equation.

a) b)

Nov 16­2:45 PM

PERMUTATIONS

A permutation is an arrangement of items where 

All of the examples that we have done so far in this unit have been examples of 

The number or permutations of n different objects taken r at a time is:

on your formula sheet!!

Math 30­1 day 2 Permutations and Factorial Notation notes.notebook

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September 07, 2016

Nov 16­2:55 PM

INVESTIGATION 1

1. Simplify the following using the permutation equation:

a) b) c)

d)                                          e)

TI 84:

TI Nspire:

Keystrokes:

Nov 16­3:04 PM

2.Solve each equation.

a) b)

Math 30­1 day 2 Permutations and Factorial Notation notes.notebook

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September 07, 2016

Nov 30­10:59 AM

c)

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INVESTIGATION 2Solve the following question in 3 different ways.

i)Using the fundamental counting principle

ii)Using the permutation equation:

iii) Using the permutation function on your calculator.  

1. How many permutations can be formed using all the letters of the word CLARINET?

Math 30­1 day 2 Permutations and Factorial Notation notes.notebook

7

September 07, 2016

Nov 16­3:18 PM

2.How many 3­letter permutations can be formed using the letters

of the word CLARINET?

Nov 16­3:19 PM

EXAMPLES:1. Determine the number of ways in which seven people can be arranged in a line.

2. Determine the number of ways in which seven people can be arranged in a line if they are selected from a group of 20 people.

http://www.google.com/imgres?start=212&num=10&hl=en&safe=active&tbo=d&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=mgm3asVgsBFZEM:&imgrefurl=http://www.ft.com/cms/s/0/1493a724­2f10­11e2­b88b­00144feabdc0.html&docid=yRme2kVfpu21cM&imgurl=http://im.ft­static.com/content/images/b73bceb6­816c­47b6­8853­fe57f856b385.img&w=600&h=338&ei=gLymUKqfBcbiiALHwIC4Aw&zoom=1&iact=hc&vpx=4&vpy=209&dur=1317&hovh=168&hovw=299&tx=157&ty=187&sig=106111925472471040228&page=9&tbnh=143&tbnw=263&ndsp=30&ved=1t:429,r:18,s:200,i:68

Math 30­1 day 2 Permutations and Factorial Notation notes.notebook

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September 07, 2016

Nov 16­3:23 PM

3. Determine the number of permutations of 5 candidates' names on a ballot box.

http://www.google.com/imgres?hl=en&safe=active&tbo=d&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=nY8mgWt1fxuuYM:&imgrefurl=http://ukhumanrightsblog.com/2010/05/09/feature­barred­voters­and­the­right­to­compensation­under­human­rights­law/&docid=lu3inRAJDQFoeM&imgurl=http://adam1cor.files.wordpress.com/2010/05/ballot_box_vote­ce­03.jpg&w=220&h=231&ei=Dr2mUMrBJYmtigL­0oCACQ&zoom=1&iact=hc&vpx=952&vpy=174&dur=1590&hovh=184&hovw=176&tx=106&ty=204&sig=106111925472471040228&page=1&tbnh=140&tbnw=130&start=0&ndsp=24&ved=1t:429,r:22,s:0,i:138

Nov 16­3:25 PM

4. How many permutations are there of the letters in the word:

a) KELOWNA                   b) REGINA

Math 30­1 day 2 Permutations and Factorial Notation notes.notebook

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September 07, 2016

Nov 16­3:25 PM

5. There are 10 different books.  How many ways can 5 of these books be arrangedon a shelf?

Nov 16­3:27 PM

6. Calculate the number of ways that an executive consisting of 4 people (president, vice president, treasurer and secretary)can be selected from a group of 20 people.

Math 30­1 day 2 Permutations and Factorial Notation notes.notebook

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September 07, 2016

Nov 16­3:28 PM

7. In Brazil, some vehicle license plates consist of any 3 differentletters followed by 4 different digits.  Find how many different license plates are possible by:

a) fundamental counting principle

b) permutations

https://www.google.com/search?num=10&hl=en&authuser=0&site=imghp&tbm=isch&source=hp&biw=1280&bih=675&q=6+people+in+a+line&oq=6+people+in+a+line&gs_l=img.3...1082.2807.0.2970.18.16.0.2.0.1.175.1647.8j8.16.0...0.0...1ac.1.pHDGVhVhVgk&safe=active#hl=en&safe=active&tbo=d&authuser=0&site=imghp&tbm=isch&sa=1&q=brazil+licence+plates&oq=brazil+licence+plates&gs_l=img.3..0i24.257714.260997.6.261128.21.12.0.6.6.0.276.1290.0j2j4.6.0...0.0...1c.1.863akRo_g0I&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&fp=4c246db500b450d3&bpcl=38625945&biw=1280&bih=675

Nov 16­3:32 PM

8. Six actors and eight actresses are available for the Jungle book play.  The playhas four male roles and three female roles.  How many different cast lists arepossible?

https://www.google.com/search?num=10&hl=en&authuser=0&site=imghp&tbm=isch&source=hp&biw=1280&bih=675&q=6+people+in+a+line&oq=6+people+in+a+line&gs_l=img.3...1082.2807.0.2970.18.16.0.2.0.1.175.1647.8j8.16.0...0.0...1ac.1.pHDGVhVhVgk&safe=active#hl=en&safe=active&tbo=d&authuser=0&site=imghp&tbm=isch&sa=1&q=jungle+book&oq=jungle+book&gs_l=img.3..0l10.174858.176859.8.177038.11.11.0.0.0.0.255.2180.0j4j7.11.0...0.0...1c.1.4T4Kf4e8tqI&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&fp=4c246db500b450d3&bpcl=38625945&biw=1280&bih=675

Math 30­1 day 2 Permutations and Factorial Notation notes.notebook

11

September 07, 2016

Nov 16­3:35 PM

9. Calculate the number of ways that an executive consisting of 4 people(president, vice president, treasurer and secretary) can be selected from a group of 20 people, if Joel must be the president.

http://www.google.com/imgres?hl=en&safe=active&tbo=d&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=cJ57AZgWFUiHwM:&imgrefurl=http://www.abdi­ecommerce10.com/naesp/p­30­set­of­four­pins­president­vice­president­secretary­and­treasurer.aspx&docid=Vbc31Ric­QWC­M&imgurl=http://www.abdi­ecommerce10.com/naesp/images/Product/medium/p110.jpg&w=200&h=219&ei=EcCmUIqvGcSfiAKcpYH4Cg&zoom=1&iact=hc&vpx=359&vpy=54&dur=1439&hovh=175&hovw=160&tx=47&ty=195&sig=106111925472471040228&page=1&tbnh=146&tbnw=133&start=0&ndsp=26&ved=1t:429,r:2,s:0,i:75

Assignment: p. 386 

  # 4d, 6d, 9, 11b, 13