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Math 301 day 3 Permutations With Constraints and Restrictions a.notebook
1
December 16, 2014
Dec 88:09 AM
LESSON 3Permutations with Restrictions
and Repetitions
Process:
Nov 153:34 PM
1. In how many ways can the letters of the word ORANGES be arranged if:
a) there are no further restrictions?
b) the first letter must be an N?
c) the vowels must all be together?
https://www.google.ca/search?num=10&hl=en&authuser=0&site=imghp&tbm=isch&source=hp&biw=1280&bih=675&q=oranges&oq=oranges&gs_l=img.3..0l10.1207.1845.0.2024.7.7.0.0.0.0.117.541.6j1.7.0...0.0...1ac.1.JCgyTM73xx4&safe=active#hl=en&safe=active&tbo=d&authuser=0&site=imghp&tbm=isch&sa=1&q=annoying+orange&oq=annoying+orange&gs_l=img.3..0j0i24l3j0i10i24l4j0i5i24.6316.10143.0.10459.10.9.0.0.0.5.820.2068.24j1j61.6.0...0.0...1c.1.mr_AnB4Def8&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&fp=ab65e995ee053246&bpcl=38625945&biw=1280&bih=675
http://www.youtube.com/watch?v=ZN5PoW7_kdA
Math 301 day 3 Permutations With Constraints and Restrictions a.notebook
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December 16, 2014
Nov 153:37 PM
2. In how many arrangements of the letters of the words BRAINS
are the vowels together?
https://www.google.ca/search?num=10&hl=en&authuser=0&site=imghp&tbm=isch&source=hp&biw=1280&bih=675&q=oranges&oq=oranges&gs_l=img.3..0l10.1207.1845.0.2024.7.7.0.0.0.0.117.541.6j1.7.0...0.0...1ac.1.JCgyTM73xx4&safe=active#hl=en&safe=active&tbo=d&authuser=0&site=imghp&tbm=isch&sa=1&q=brains&oq=brains&gs_l=img.3..0l10.94042.94633.2.94824.6.6.0.0.0.0.256.399.0j1j1.2.0...0.0...1c.1.AD3Dp6wVOzI&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&fp=c1922a5d14787d15&bpcl=38625945&biw=1280&bih=675
Nov 153:39 PM
3. Find the number of permutations of the letters in the word KITCHEN if:
a) the letters K, C, and N must be together but not necessarily in that order?
b) the vowels must not be together
http://www.google.ca/imgres?hl=en&safe=active&tbo=d&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=ylvxEuUK3SgCaM:&imgrefurl=http://gillinghamcabinets.com/&docid=GLpePgmJS5gFlM&imgurl=http://gillinghamcabinets.com/images/kitchen_cabinets_show/kitchen_cabinets_01.jpg&w=550&h=370&ei=WlUOnpC6ayigKer4HIBQ&zoom=1&iact=hc&vpx=635&vpy=63&dur=321&hovh=184&hovw=274&tx=104&ty=104&sig=109971733282591085494&page=1&tbnh=144&tbnw=204&start=0&ndsp=25&ved=1t:429,r:4,s:0,i:79
Math 301 day 3 Permutations With Constraints and Restrictions a.notebook
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December 16, 2014
Nov 153:44 PM
4. In how many ways can 3 girls and 4 boys be arranged in a row if no
two people of the same gender can sit together?
1 2 3 4 1 2 3
Nov 153:47 PM
5. Determine the number of distinguishable arrangements of the letters
in the word EDSON if the consonants are to be kept together.
Math 301 day 3 Permutations With Constraints and Restrictions a.notebook
4
December 16, 2014
Dec 87:37 AM
Nov 154:05 PM
PERMUTATIONS INVOLVING IDENTICAL OBJECTS
There will be fewer permutations of a number of objects when some of theobjects are identical since a new arrangement will not be formed when the identical objects are interchanged.
The number of permutations of n objects taken n at time, if there are a alikeof one kind, b alike of another kind, c alike of another kind, etc. is:
http://www.google.ca/imgres?hl=en&safe=active&tbo=d&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=iPIa91bipjJj1M:&imgrefurl=http://smartactors.com/2011/11/howdyougetsosmart/&docid=vXMNggHPGwSrOM&imgurl=http://smartactors.com/Blogs%252520%252520Picture/now%252520i%252520get%252520it.gif&w=1315&h=876&ei=gHalUIrNPOKvigLkxYG4Cg&zoom=1&iact=hc&vpx=299&vpy=155&dur=155&hovh=183&hovw=275&tx=198&ty=126&sig=109971733282591085494&page=1&tbnh=134&tbnw=201&start=0&ndsp=21&ved=1t:429,r:2,s:0,i:73
Math 301 day 3 Permutations With Constraints and Restrictions a.notebook
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December 16, 2014
Nov 1611:33 AM
EXAMPLES:
1. Determine the number of permutations of all the letters in the word PARALLEL.
2. Determine the number of permutations of all the letters in theword MATHEMATICS.
do on the board
Nov 1611:35 AM
3. A teacher has two exams to be administered to a class of 20 students.The teacher has 12 exams of one type and 8 exams of another type.How many different ways can these exams be given to the students?
http://www.google.ca/imgres?num=10&hl=en&safe=active&tbo=d&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=Twe12nBL_450GM:&imgrefurl=http://www.ucdsb.on.ca/school/sla/aboutus/Pages/ExamSchedule.aspx&docid=BIcwZYWpBSe1bM&imgurl=http://www.ucdsb.on.ca/school/sla/aboutus/PublishingImages/Exam2.gif&w=407&h=580&ei=x4emUOqyI4rWiwLtvoHAAw&zoom=1&iact=rc&dur=283&sig=109971733282591085494&page=1&tbnh=147&tbnw=103&start=0&ndsp=26&ved=1t:429,r:2,s:0,i:76&tx=38&ty=107
Math 301 day 3 Permutations With Constraints and Restrictions a.notebook
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December 16, 2014
Nov 1611:37 AM
4. How many ways can 4 red, 2 blue, and 3 green marbles be distributedamong 9 children, if each child is to receive one marble?
http://www.google.ca/imgres?hl=en&safe=active&tbo=d&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=ouQdqMTmp13d9M:&imgrefurl=http://www.123rf.com/photo_4776590_threeroundmarblesredgreenandblueonwhitebackground.html&docid=bbIO0lyB1PPqEM&imgurl=http://us.123rf.com/400wm/400/400/sundeepgoel/sundeepgoel0904/sundeepgoel090400008/4776590threeroundmarblesredgreenandblueonwhitebackground.jpg&w=400&h=267&ei=NoimUIHUHoG1iwLO8IDAAg&zoom=1&iact=hc&vpx=4&vpy=156&dur=1388&hovh=183&hovw=275&tx=155&ty=208&sig=109971733282591085494&page=1&tbnh=136&tbnw=204&start=0&ndsp=18&ved=1t:429,r:0,s:0,i:67
Nov 1611:39 AM
5. There are 3 blue flags, 3 white flags, and 2 red flags. How many different signalscan be constructed by making a vertical display of 8 flags?
http://www.google.ca/imgres?num=10&hl=en&safe=active&tbo=d&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=UJ672JBRzm60eM:&imgrefurl=http://www.cbc.ca/news/canada/story/2010/05/26/fg8huntsvilleg20toronto.html&docid=CWIKf9L6NIFhM&imgurl=http://www.cbc.ca/gfx/images/news/photos/2010/06/02/g8flags190cp165789.jpg&w=1976&h=888&ei=wIimUNDJDIeYiAKe8oDIDw&zoom=1&iact=hc&vpx=904&vpy=42&dur=1499&hovh=150&hovw=335&tx=139&ty=171&sig=109971733282591085494&sqi=2&page=1&tbnh=139&tbnw=277&start=0&ndsp=18&ved=1t:429,r:17,s:0,i:118
Math 301 day 3 Permutations With Constraints and Restrictions a.notebook
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December 16, 2014
Nov 1611:42 AM
6. A builder has three models of homes from which customers can choose:A, B, or C. On one side of a street, the builder sold three model A homes, four model B homes, and two model C homes. In how many ways can the homes be arranged along the street?
http://www.google.ca/imgres?hl=en&safe=active&tbo=d&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=YGvRVMe0vrDJOM:&imgrefurl=http://northropteam.com/blog/2012/07/13/introducingnewconstructionsinglefamilyhomesinclarksburgmd/&docid=MBUWZbImE26GOM&imgurl=http://northropteam.com/blog/wpcontent/uploads/2012/07/GatewayCommons3ModelsAvailable1024x282.jpg&w=1024&h=282&ei=WYmmUI34KqTtigK75oC4Bw&zoom=1&iact=hc&vpx=652&vpy=208&dur=1467&hovh=118&hovw=428&tx=196&ty=142&sig=109971733282591085494&page=1&tbnh=74&tbnw=242&start=0&ndsp=25&ved=1t:429,r:23,s:0,i:140
Nov 1611:45 AM
7. How many arrangements of the word POPPIES can be madeunder each of the following conditions?
a) without restrictions
b) if each arrangement begins with a P
c) if the first two letters are P
d) if all the P's are together
http://www.google.ca/imgres?hl=en&safe=active&tbo=d&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=3l9JShha3bZTM:&imgrefurl=http://www.416florist.com/flowerblog/holidayflowers/historyofpoppiespartone.html&docid=VnQJqsPluJIlqM&imgurl=http://www.416florist.com/flowerblog/wpcontent/uploads/2010/10/PoppyField.jpg&w=961&h=643&ei=RIqmUNeYE8yuigK88IDoDQ&zoom=1&iact=hc&vpx=964&vpy=288&dur=1964&hovh=184&hovw=275&tx=77&ty=203&sig=109971733282591085494&page=3&tbnh=155&tbnw=246&start=62&ndsp=28&ved=1t:429,r:89,s:0,i:338
Math 301 day 3 Permutations With Constraints and Restrictions a.notebook
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December 16, 2014
Nov 1611:54 AM
8. An airline pilot reported her itinerary for 7 days. She spent1 day in Winnipeg, 1 day in Regina, 2 days in Edmonton, and3 days in Yellowknife.
a) How many different itineraries are possible?
b) What difference would it make if the first and last dayhad to be spent in Yellowknife?
Nov 163:37 PM