Download - 11 x1 t05 02 permutations ii (2012)
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Case 3: Ordered Sets of n Objects, Not All DifferentPermutations
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Case 3: Ordered Sets of n Objects, Not All Different(i.e. some of the objects are the same)
Permutations
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Case 3: Ordered Sets of n Objects, Not All Different(i.e. some of the objects are the same)
2 objectsPermutations
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Case 3: Ordered Sets of n Objects, Not All Different(i.e. some of the objects are the same)
2 objectsall different
A B
B A
Permutations
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Case 3: Ordered Sets of n Objects, Not All Different(i.e. some of the objects are the same)
2 objectsall different
A B
B A22!
Permutations
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Case 3: Ordered Sets of n Objects, Not All Different(i.e. some of the objects are the same)
2 objectsall different
A B
B A22!
2 sameA A
1
Permutations
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Case 3: Ordered Sets of n Objects, Not All Different(i.e. some of the objects are the same)
2 objectsall different
A B
B A22!
2 sameA A
13 objects
Permutations
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Case 3: Ordered Sets of n Objects, Not All Different(i.e. some of the objects are the same)
2 objectsall different
A B
B A22!
2 sameA A
13 objectsall differentA B C
A C B
B A C
B C A
C A B
C B A
Permutations
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Case 3: Ordered Sets of n Objects, Not All Different(i.e. some of the objects are the same)
2 objectsall different
A B
B A22!
2 sameA A
13 objectsall differentA B C
A C B
B A C
B C A
C A B
C B A63!
Permutations
![Page 10: 11 x1 t05 02 permutations ii (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052410/55614b7bd8b42a857d8b4a60/html5/thumbnails/10.jpg)
Case 3: Ordered Sets of n Objects, Not All Different(i.e. some of the objects are the same)
2 objectsall different
A B
B A22!
2 sameA A
13 objectsall differentA B C
A C B
B A C
B C A
C A B
C B A63!
2 sameA A B
A B A
B A A
3
Permutations
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Case 3: Ordered Sets of n Objects, Not All Different(i.e. some of the objects are the same)
2 objectsall different
A B
B A22!
2 sameA A
13 objectsall differentA B C
A C B
B A C
B C A
C A B
C B A63!
2 sameA A B
A B A
B A A
3
3 sameA A A
1
Permutations
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4 objects
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4 objectsall different
A B C DA B D CA C B DA C D BA D B CA D C BB A C DB A D CB C A DB C D AB D A CB D A B
C B A DC B D AC A B DC A D BC D B AC D A BD A C BD A B CD C A BD C B AD B A CD B A B
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4 objectsall different
A B C DA B D CA C B DA C D BA D B CA D C BB A C DB A D CB C A DB C D AB D A CB D A B
24 4!
C B A DC B D AC A B DC A D BC D B AC D A BD A C BD A B CD C A BD C B AD B A CD B A B
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4 objectsall different
A B C DA B D CA C B DA C D BA D B CA D C BB A C DB A D CB C A DB C D AB D A CB D A B
24 4!
2 sameA A B CA A C BA B A CA B C AA C A BA C B AB A A CB A C AB C A AC A A BC A B AC B A A
12
C B A DC B D AC A B DC A D BC D B AC D A BD A C BD A B CD C A BD C B AD B A CD B A B
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4 objectsall different
A B C DA B D CA C B DA C D BA D B CA D C BB A C DB A D CB C A DB C D AB D A CB D A B
24 4!
2 sameA A B CA A C BA B A CA B C AA C A BA C B AB A A CB A C AB C A AC A A BC A B AC B A A
12
3 sameA A A B
A A B A
A B A A
B A A A
4
C B A DC B D AC A B DC A D BC D B AC D A BD A C BD A B CD C A BD C B AD B A CD B A B
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4 objectsall different
A B C DA B D CA C B DA C D BA D B CA D C BB A C DB A D CB C A DB C D AB D A CB D A B
24 4!
2 sameA A B CA A C BA B A CA B C AA C A BA C B AB A A CB A C AB C A AC A A BC A B AC B A A
12
3 sameA A A B
A A B A
A B A A
B A A A
4
C B A DC B D AC A B DC A D BC D B AC D A BD A C BD A B CD C A BD C B AD B A CD B A B
4 sameA A A A
1
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If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
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If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
x!n!
tsArrangemen ofNumber
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If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
x!n!
tsArrangemen ofNumber objects
arrangingofwaysn
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If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
x!n!
tsArrangemen ofNumber objects
arrangingofwaysn
objects like thearrangingofways
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If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
x!n!
tsArrangemen ofNumber objects
arrangingofwaysn
objects like thearrangingofways
e.g. How many different words can be formed using all of the letters in the word
CONNAUGHTON ?
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If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
x!n!
tsArrangemen ofNumber objects
arrangingofwaysn
objects like thearrangingofways
e.g. How many different words can be formed using all of the letters in the word
CONNAUGHTON ?
!3!2!11 Words
![Page 24: 11 x1 t05 02 permutations ii (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052410/55614b7bd8b42a857d8b4a60/html5/thumbnails/24.jpg)
If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
x!n!
tsArrangemen ofNumber objects
arrangingofwaysn
objects like thearrangingofways
e.g. How many different words can be formed using all of the letters in the word
CONNAUGHTON ?
!3!2!11 Words
sO' twofor the2!
![Page 25: 11 x1 t05 02 permutations ii (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052410/55614b7bd8b42a857d8b4a60/html5/thumbnails/25.jpg)
If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
x!n!
tsArrangemen ofNumber objects
arrangingofwaysn
objects like thearrangingofways
e.g. How many different words can be formed using all of the letters in the word
CONNAUGHTON ?
!3!2!11 Words
sO' twofor the2! sN'threefor the3!
![Page 26: 11 x1 t05 02 permutations ii (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052410/55614b7bd8b42a857d8b4a60/html5/thumbnails/26.jpg)
If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
x!n!
tsArrangemen ofNumber objects
arrangingofwaysn
objects like thearrangingofways
e.g. How many different words can be formed using all of the letters in the word
CONNAUGHTON ?
!3!2!11 Words
sO' twofor the2! sN'threefor the3!3326400
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The letters A, E, I, O and U are vowels2001 Extension 1 HSC Q2c)
(i) How many arrangements of the letters in the word ALGEBRAIC are possible?
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The letters A, E, I, O and U are vowels2001 Extension 1 HSC Q2c)
(i) How many arrangements of the letters in the word ALGEBRAIC are possible?
!2!9 Words
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The letters A, E, I, O and U are vowels2001 Extension 1 HSC Q2c)
(i) How many arrangements of the letters in the word ALGEBRAIC are possible?
!2!9 Words
181440
![Page 30: 11 x1 t05 02 permutations ii (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052410/55614b7bd8b42a857d8b4a60/html5/thumbnails/30.jpg)
The letters A, E, I, O and U are vowels2001 Extension 1 HSC Q2c)
(i) How many arrangements of the letters in the word ALGEBRAIC are possible?
!2!9 Words
181440
(ii) How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2nd, 3rd, 5th, and 8th
positions?
![Page 31: 11 x1 t05 02 permutations ii (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052410/55614b7bd8b42a857d8b4a60/html5/thumbnails/31.jpg)
The letters A, E, I, O and U are vowels2001 Extension 1 HSC Q2c)
(i) How many arrangements of the letters in the word ALGEBRAIC are possible?
!2!9 Words
181440
(ii) How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2nd, 3rd, 5th, and 8th
positions?!2!4 Words !5
![Page 32: 11 x1 t05 02 permutations ii (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052410/55614b7bd8b42a857d8b4a60/html5/thumbnails/32.jpg)
The letters A, E, I, O and U are vowels2001 Extension 1 HSC Q2c)
(i) How many arrangements of the letters in the word ALGEBRAIC are possible?
!2!9 Words
181440
(ii) How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2nd, 3rd, 5th, and 8th
positions?!2!4 Words
vowels theplacingof waysofNumber
!5
![Page 33: 11 x1 t05 02 permutations ii (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052410/55614b7bd8b42a857d8b4a60/html5/thumbnails/33.jpg)
The letters A, E, I, O and U are vowels2001 Extension 1 HSC Q2c)
(i) How many arrangements of the letters in the word ALGEBRAIC are possible?
!2!9 Words
181440
(ii) How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2nd, 3rd, 5th, and 8th
positions?!2!4 Words
vowels theplacingof waysofNumber
consonants theplacing ofwaysofNumber
!5
![Page 34: 11 x1 t05 02 permutations ii (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052410/55614b7bd8b42a857d8b4a60/html5/thumbnails/34.jpg)
The letters A, E, I, O and U are vowels2001 Extension 1 HSC Q2c)
(i) How many arrangements of the letters in the word ALGEBRAIC are possible?
!2!9 Words
181440
(ii) How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2nd, 3rd, 5th, and 8th
positions?!2!4 Words
vowels theplacingof waysofNumber
consonants theplacing ofwaysofNumber
!5
1440
![Page 35: 11 x1 t05 02 permutations ii (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052410/55614b7bd8b42a857d8b4a60/html5/thumbnails/35.jpg)
The letters A, E, I, O and U are vowels2001 Extension 1 HSC Q2c)
(i) How many arrangements of the letters in the word ALGEBRAIC are possible?
!2!9 Words
181440
(ii) How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2nd, 3rd, 5th, and 8th
positions?!2!4 Words
vowels theplacingof waysofNumber
consonants theplacing ofwaysofNumber
!5
1440
Exercise 10F; odd