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# 11X1 T06 02 permutations II (2010)

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• 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