11X1 T05 02 permutations II (2011)

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  • 1. Permutations Not All DifferentCase 3: Ordered Sets of n Objects,

2. Permutations Not All DifferentCase 3: Ordered Sets of n Objects,(i.e. some of the objects are the same) 3. 2 objects Permutations Not All DifferentCase 3: Ordered Sets of n Objects,(i.e. some of the objects are the same) 4. 2 objects Permutations Not All DifferentCase 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 DifferentCase 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 DifferentCase 3: Ordered Sets of n Objects,all different 2 same (i.e. some of the objects are the same)A BA A B A 2! 2 1 7. 2 objects Permutations Not All DifferentCase 3: Ordered Sets of n Objects,all different 2 same (i.e. some of the objects are the same)A BA A B A 2! 2 1 3 objects 8. 2 objects Permutations Not All DifferentCase 3: Ordered Sets of n Objects,all different 2 same (i.e. some of the objects are the same)A BA A B A2! 21 3 objectsall different A B CA C BB A CB C AC A BC B A 9. 2 objects Permutations Not All DifferentCase 3: Ordered Sets of n Objects,all different 2 same (i.e. some of the objects are the same)A BA A B A2! 21 3 objectsall different A B CA C BB A CB C AC A BC B A 3! 6 10. 2 objects Permutations Not All DifferentCase 3: Ordered Sets of n Objects,all different 2 same (i.e. some of the objects are the same)A BA A B A2! 21 3 objectsall different2 same A B C A A BA C BA B AB A CB A AB C AC A BC B A 3! 63 11. 2 objects Permutations Not All DifferentCase 3: Ordered Sets of n Objects,all different 2 same (i.e. some of the objects are the same)A BA A B A2! 21 3 objectsall different2 same3 same A B C A A B A A AA C BA B AB A CB A AB C AC A BC B A 3! 63 1 12. 4 objects 13. 4 objectsall differentA B C DCB A DA B D CCB D AA C B DCA B DA C D BCA D BA D B CCD B AA D C BCD A BB A C DDA C BB A D CDA B CB C A DDC A BB C D ADC B AB D A CDB A CB D A BDB A B 14. 4 objectsall differentA B C DCB A DA B D CCB D AA C B DCA B DA C D BCA D BA D B CCD B AA D C BCD A BB A C DDA C BB A D CDA B CB C A DDC A BB C D ADC B AB D A CDB A CB D A BDB A B4! 24 15. 4 objectsall different 2 sameA B C DCB A D A A BCA B D CCB D A A A CBA C B DCA B D A B ACA C D BCA D B A B CAA D B CCD B A A C ABA D C BCD A B A C BAB A C DDA C B B A ACB A D CDA B C B A CAB C A DDC A B B C AAB C D ADC B A C A ABB D A CDB A C C A BAB D A BDB A B C B AA4! 2412 16. 4 objectsall different 2 same3 sameA B C DCB A D A A BC A A A BA B D CCB D A A A CB A A B AA C B DCA B D A B AC A B A AA C D BCA D B A B CAA D B CCD B A A C AB B A A AA D C BCD A B A C BA4B A C DDA C B B A ACB A D CDA B C B A CAB C A DDC A B B C AAB C D ADC B A C A ABB D A CDB A C C A BAB D A BDB A B C B AA4! 2412 17. 4 objectsall different 2 same3 sameA B C DCB A D A A BC A A A BA B D CCB D A A A CB A A B AA C B DCA B D A B AC A B A AA C D BCA D B A B CAA D B CCD B A A C AB B A A AA D C BCD A B A C BA4B A C DDA C B B A ACB A D CDA B C B A CAB C A DDC A B B C AAB C D ADC B A C A ABB D A CDB A C C A BA4 sameB D A BDB A B C B AA A A A A4! 24121 18. If we arrange n objects in a line, of which x are alike, the number ofways we could arrange them are; 19. If we arrange n objects in a line, of which x are alike, the number ofways 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 ofways we could arrange them are; ways of arrangingn!n objects Number of Arrangements x! 21. If we arrange n objects in a line, of which x are alike, the number ofways we could arrange them are; ways of arrangingn!n objects Number of Arrangements x!ways of arrangingthe 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 objectsNumber of Arrangements x!ways of arranging the like objectse.g. How many different words can be formed using all of the letters in the wordCONNAUGHTON ? 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 objectsNumber of Arrangements x!ways of arranging the like objectse.g. How many different words can be formed using all of the letters in the wordCONNAUGHTON ?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 objectsNumber of Arrangements x!ways of arranging the like objectse.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 objectsNumber of Arrangements x!ways of arranging the like objectse.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 s3! 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 objectsNumber of Arrangements x!ways of arranging the like objectse.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 s3! 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 ALGEBRAICare 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 ALGEBRAICare 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 ALGEBRAICare 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 ALGEBRAICare possible? 9! Words 2! 181440(ii) How many arrangements of the letters in the word ALGEBRAICare possible if the vowels must occupy the 2nd, 3rd, 5th, and 8thpositions? 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 ALGEBRAICare possible? 9! Words 2! 181440(ii) How many arrangements of the letters in the word ALGEBRAICare possible if the vowels must occupy the 2nd, 3rd, 5th, and 8thpositions?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 ALGEBRAICare possible? 9! Words 2! 181440(ii) How many arrangements of the letters in the word ALGEBRAICare possible if the vowels must occupy the 2nd, 3rd, 5th, and 8thpositions?4! Words 5!2!Number of ways ofplacing 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 ALGEBRAICare possible? 9! Words 2! 181440(ii) How many arrangements of the letters in the word ALGEBRAICare possible if the vowels must occupy the 2nd, 3rd, 5th, and 8thpositions?4! Words 5!2!Number of ways ofNumber of ways ofplacing the vowelsplacing 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 ALGEBRAICare possible? 9! Words 2! 181440(ii) How many arrangements of the letters in the word ALGEBRAICare possible if the vowels must occupy the 2nd, 3rd, 5th, and 8thpositions?4! Words 5!2!Number of ways of 1440 Number of ways ofplacing the vowelsplacing 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 ALGEBRAICare possible? 9! Words 2! 181440(ii) How many arrangements of the letters in the word ALGEBRAICare possible if the vowels must occupy the 2nd, 3rd, 5th, and 8thpositions?4! Words 5!2!Number of ways of 1440 Number of ways ofplacing the vowelsplacing the consonants Exercise 10F; odd