12X1 T09 04 permutations II

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12X1 T09 04 permutations II

  1. 1. Case 3: Ordered Sets of n Objects, Not All Different Permutations
  2. 2. Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) Permutations
  3. 3. Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) 2 objects Permutations
  4. 4. Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) 2 objects all different A B B A Permutations
  5. 5. Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) 2 objects all different A B B A Permutations
  6. 6. Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) 2 objects all different A B B A 2 same A A Permutations
  7. 7. Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) 2 objects all different A B B A 2 same A A 3 objects Permutations
  8. 8. Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) 2 objects all different A B B A 2 same A A 3 objects all different A B C A C B B A C B C A C A B C B A Permutations
  9. 9. Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) 2 objects all different A B B A 2 same A A 3 objects all different A B C A C B B A C B C A C A B C B A Permutations
  10. 10. Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) 2 objects all different A B B A 2 same A A 3 objects all different A B C A C B B A C B C A C A B C B A 2 same A A B A B A B A A Permutations
  11. 11. Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) 2 objects all different A B B A 2 same A A 3 objects all different A B C A C B B A C B C A C A B C B A 2 same A A B A B A B A A 3 same A A A Permutations
  12. 12. 4 objects
  13. 13. 4 objects all different A B C D A B D C A C B D A C D B A D B C A D C B B A C D B A D C B C A D B C D A B D A C B D A B C B A D C B D A C A B D C A D B C D B A C D A B D A C B D A B C D C A B D C B A D B A C D B A B
  14. 14. 4 objects all different A B C D A B D C A C B D A C D B A D B C A D C B B A C D B A D C B C A D B C D A B D A C B D A B C B A D C B D A C A B D C A D B C D B A C D A B D A C B D A B C D C A B D C B A D B A C D B A B
  15. 15. 4 objects all different A B C D A B D C A C B D A C D B A D B C A D C B B A C D B A D C B C A D B C D A B D A C B D A B 2 same A A B C A A C B A B A C A B C A A C A B A C B A B A A C B A C A B C A A C A A B C A B A C B A A C B A D C B D A C A B D C A D B C D B A C D A B D A C B D A B C D C A B D C B A D B A C D B A B
  16. 16. 4 objects all different A B C D A B D C A C B D A C D B A D B C A D C B B A C D B A D C B C A D B C D A B D A C B D A B 2 same A A B C A A C B A B A C A B C A A C A B A C B A B A A C B A C A B C A A C A A B C A B A C B A A 3 same A A A B A A B A A B A A B A A A C B A D C B D A C A B D C A D B C D B A C D A B D A C B D A B C D C A B D C B A D B A C D B A B
  17. 17. 4 objects all different A B C D A B D C A C B D A C D B A D B C A D C B B A C D B A D C B C A D B C D A B D A C B D A B 2 same A A B C A A C B A B A C A B C A A C A B A C B A B A A C B A C A B C A A C A A B C A B A C B A A 3 same A A A B A A B A A B A A B A A A C B A D C B D A C A B D C A D B C D B A C D A B D A C B D A B C D C A B D C B A D B A C D B A B 4 same A A A A
  18. 18. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
  19. 19. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
  20. 20. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
  21. 21. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
  22. 22. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; e.g. How many different words can be formed using all of the letters in the word CONNAUGHTON ?
  23. 23. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; e.g. How many different words can be formed using all of the letters in the word CONNAUGHTON ?
  24. 24. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; e.g. How many different words can be formed using all of the letters in the word CONNAUGHTON ?
  25. 25. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; e.g. How many different words can be formed using all of the letters in the word CONNAUGHTON ?
  26. 26. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are; e.g. How many different words can be formed using all of the letters in the word CONNAUGHTON ?
  27. 27. The letters A, E, I, O and U are vowels 2001 Extension 1 HSC Q2c) ( i ) How many arrangements of the letters in the word ALGEBRAIC are possible?
  28. 28. The letters A, E, I, O and U are vowels 2001 Extension 1 HSC Q2c) ( i ) How many arrangements of the letters in the word ALGEBRAIC are possible?
  29. 29. The letters A, E, I, O and U are vowels 2001 Extension 1 HSC Q2c) ( i ) How many arrangements of the letters in the word ALGEBRAIC are possible?
  30. 30. The letters A, E, I, O and U are vowels 2001 Extension 1 HSC Q2c) ( i ) How many arrangements of the letters in the word ALGEBRAIC are possible? ( ii ) How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2 nd , 3 rd , 5 th , and 8 th positions?
  31. 31. The letters A, E, I, O and U are vowels 2001 Extension 1 HSC Q2c) ( i ) How many arrangements of the letters in the word ALGEBRAIC are possible? ( ii ) How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2 nd , 3 rd , 5 th , and 8 th positions?
  32. 32. The letters A, E, I, O and U are vowels 2001 Extension 1 HSC Q2c) ( i ) How many arrangements of the letters in the word ALGEBRAIC are possible? ( ii ) How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2 nd , 3 rd , 5 th , and 8 th positions?
  33. 33. The letters A, E, I, O and U are vowels 2001 Extension 1 HSC Q2c) ( i ) How many arrangements of the letters in the word ALGEBRAIC are possible? ( ii ) How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2 nd , 3 rd , 5 th , and 8 th positions?
  34. 34. The letters A, E, I, O and U are vowels 2001 Extension 1 HSC Q2c) ( i ) How many arrangements of the letters in the word ALGEBRAIC are possible? ( ii ) How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2 nd , 3 rd , 5 th , and 8 th positions?
  35. 35. The letters A, E, I, O and U are vowels 2001 Extension 1 HSC Q2c) ( i ) How many arrangements of the letters in the word ALGEBRAIC are possible? ( ii ) How many arrangements of the letters in the word ALGEBRAIC are possible if the vowels must occupy the 2 nd , 3 rd , 5 th , and 8 th positions? Exercise 10F; odd

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