Your SlideShare is downloading. ×
0
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
11X1 T06 02 permutations II (2010)
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

11X1 T06 02 permutations II (2010)

386

Published on

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
386
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
27
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Permutations Not All Different Case 3: Ordered Sets of n Objects,
  • 2. Permutations Not All Different Case 3: Ordered Sets of n Objects, (i.e. some of the objects are the same)
  • 3. 2 objects Permutations Not All Different Case 3: Ordered Sets of n Objects, (i.e. some of the objects are the same)
  • 4. 2 objects Permutations Not All Different Case 3: Ordered Sets of n Objects, all different (i.e. some of the objects are the same) A B B A
  • 5. 2 objects Permutations Not All Different Case 3: Ordered Sets of n Objects, all different (i.e. some of the objects are the same) A B B A 2! 2
  • 6. 2 objects Permutations Not All Different Case 3: Ordered Sets of n Objects, all different 2 same (i.e. some of the objects are the same) A B A A B A 2! 2 1
  • 7. 2 objects Permutations Not All Different Case 3: Ordered Sets of n Objects, all different 2 same (i.e. some of the objects are the same) A B A A B A 2! 2 1 3 objects
  • 8. 2 objects Permutations Not All Different Case 3: Ordered Sets of n Objects, all different 2 same (i.e. some of the objects are the same) A B A A B A 2! 2 1 3 objects all different A B C A C B B A C B C A C A B C B A
  • 9. 2 objects Permutations Not All Different Case 3: Ordered Sets of n Objects, all different 2 same (i.e. some of the objects are the same) A B A A B A 2! 2 1 3 objects all different A B C A C B B A C B C A C A B C B A 3! 6
  • 10. 2 objects Permutations Not All Different Case 3: Ordered Sets of n Objects, all different 2 same (i.e. some of the objects are the same) A B A A B A 2! 2 1 3 objects all different 2 same A B C A A B A C B A B A B A C B A A B C A C A B C B A 3! 6 3
  • 11. 2 objects Permutations Not All Different Case 3: Ordered Sets of n Objects, all different 2 same (i.e. some of the objects are the same) A B A A B A 2! 2 1 3 objects all different 2 same 3 same A B C A A B A A A A C B A B A B A C B A A B C A C A B C B A 3! 6 3 1
  • 12. 4 objects
  • 13. 4 objects all different A B C D C B A D A B D C C B D A A C B D C A B D A C D B C A D B A D B C C D B A A D C B C D A B B A C D D A C B B A D C D A B C B C A D D C A B B C D A D C B A B D A C D B A C B D A B D B A B
  • 14. 4 objects all different A B C D C B A D A B D C C B D A A C B D C A B D A C D B C A D B A D B C C D B A A D C B C D A B B A C D D A C B B A D C D A B C B C A D D C A B B C D A D C B A B D A C D B A C B D A B D B A B 4! 24
  • 15. 4 objects all different 2 same A B C D C B A D A A B C A B D C C B D A A A C B A C B D C A B D A B A C A C D B C A D B A B C A A D B C C D B A A C A B A D C B C D A B A C B A B A C D D A C B B A A C B A D C D A B C B A C A B C A D D C A B B C A A B C D A D C B A C A A B B D A C D B A C C A B A B D A B D B A B C B A A 4! 24 12
  • 16. 4 objects all different 2 same 3 same A B C D C B A D A A B C A A A B A B D C C B D A A A C B A A B A A C B D C A B D A B A C A B A A A C D B C A D B A B C A A D B C C D B A A C A B B A A A A D C B C D A B A C B A 4 B A C D D A C B B A A C B A D C D A B C B A C A B C A D D C A B B C A A B C D A D C B A C A A B B D A C D B A C C A B A B D A B D B A B C B A A 4! 24 12
  • 17. 4 objects all different 2 same 3 same A B C D C B A D A A B C A A A B A B D C C B D A A A C B A A B A A C B D C A B D A B A C A B A A A C D B C A D B A B C A A D B C C D B A A C A B B A A A A D C B C D A B A C B A 4 B A C D D A C B B A A C B A D C D A B C B A C A B C A D D C A B B C A A B C D A D C B A C A A B B D A C D B A C C A B A 4 same B D A B D B A B C B A A A A A A 4! 24 12 1
  • 18. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
  • 19. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; n! Number of Arrangements  x!
  • 20. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; ways of arranging n! n objects Number of Arrangements  x!
  • 21. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; ways of arranging n! n objects Number of Arrangements  x! ways of arranging the like objects
  • 22. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; ways of arranging n! n objects Number of Arrangements  x! ways of arranging the like objects e.g. How many different words can be formed using all of the letters in the word CONNAUGHTON ?
  • 23. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; ways of arranging n! n objects Number of Arrangements  x! ways of arranging the like objects e.g. How many different words can be formed using all of the letters in the word CONNAUGHTON ? 11! Words  2!3!
  • 24. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; ways of arranging n! n objects Number of Arrangements  x! ways of arranging the like objects e.g. How many different words can be formed using all of the letters in the word CONNAUGHTON ? 11! Words  2!3! 2! for the two O' s
  • 25. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; ways of arranging n! n objects Number of Arrangements  x! ways of arranging the like objects e.g. How many different words can be formed using all of the letters in the word CONNAUGHTON ? 11! Words  2!3! 2! for the two O' s 3! for the three N' s
  • 26. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; ways of arranging n! n objects Number of Arrangements  x! ways of arranging the like objects e.g. How many different words can be formed using all of the letters in the word CONNAUGHTON ? 11! Words  2!3!  3326400 2! for the two O' s 3! for the three N' s
  • 27. 2001 Extension 1 HSC Q2c) The letters A, E, I, O and U are vowels (i) How many arrangements of the letters in the word ALGEBRAIC are possible?
  • 28. 2001 Extension 1 HSC Q2c) The letters A, E, I, O and U are vowels (i) How many arrangements of the letters in the word ALGEBRAIC are possible? 9! Words  2!
  • 29. 2001 Extension 1 HSC Q2c) The letters A, E, I, O and U are vowels (i) How many arrangements of the letters in the word ALGEBRAIC are possible? 9! Words  2!  181440
  • 30. 2001 Extension 1 HSC Q2c) The letters A, E, I, O and U are vowels (i) How many arrangements of the letters in the word ALGEBRAIC are possible? 9! Words  2!  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?
  • 31. 2001 Extension 1 HSC Q2c) The letters A, E, I, O and U are vowels (i) How many arrangements of the letters in the word ALGEBRAIC are possible? 9! Words  2!  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? 4! Words   5! 2!
  • 32. 2001 Extension 1 HSC Q2c) The letters A, E, I, O and U are vowels (i) How many arrangements of the letters in the word ALGEBRAIC are possible? 9! Words  2!  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? 4! Words   5! 2! Number of ways of placing the vowels
  • 33. 2001 Extension 1 HSC Q2c) The letters A, E, I, O and U are vowels (i) How many arrangements of the letters in the word ALGEBRAIC are possible? 9! Words  2!  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? 4! Words   5! 2! Number of ways of Number of ways of placing the vowels placing the consonants
  • 34. 2001 Extension 1 HSC Q2c) The letters A, E, I, O and U are vowels (i) How many arrangements of the letters in the word ALGEBRAIC are possible? 9! Words  2!  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? 4! Words   5! 2! Number of ways of  1440 Number of ways of placing the vowels placing the consonants
  • 35. 2001 Extension 1 HSC Q2c) The letters A, E, I, O and U are vowels (i) How many arrangements of the letters in the word ALGEBRAIC are possible? 9! Words  2!  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? 4! Words   5! 2! Number of ways of  1440 Number of ways of placing the vowels placing the consonants Exercise 10F; odd

×