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Case 3: Ordered Sets of n Objects, Not All Different Permutations
Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) Permutations
Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) 2 objects Permutations
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
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
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
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
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
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
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
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
4 objects
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
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
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
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 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
If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
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 ?
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 ?
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 ?
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 ?
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 ?
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?
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?
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?
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?
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?
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?
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?
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?
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
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I
12X1 T09 03 permutations I

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12X1 T09 03 permutations I

  • 1. Case 3: Ordered Sets of n Objects, Not All Different Permutations
  • 2. Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) Permutations
  • 3. Case 3: Ordered Sets of n Objects, Not All Different (i.e. some of the objects are the same) 2 objects Permutations
  • 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. 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. 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. 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. 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. 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. 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. 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
  • 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. 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. 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. 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. 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. 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;
  • 20. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
  • 21. If we arrange n objects in a line, of which x are alike, the number of ways we could arrange them are;
  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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