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Math 301 day 2 Permutations and Factorial Notation notes.notebook
1
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
2
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)
Nov 163:08 PM
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
10
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
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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