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  • Level: GCSE
  • Subject: Maths
  • Word count: 1357

Emma's Dilemma

Extracts from this document...

Introduction

David Leiwy

EMMA'S DILEMMA

image00.png

4 LETTER NAME WITH 2 LETTER THE SAME

EMMA

  1. EMMA
  2. EMAM
  3. EAMM
  4. MEMA
  5. MEAM
  6. MMEA
  7. MMAE
  8. MAME
  9. MAEM
  10. AEMM
  11. AMEM

12) AMME            

4 LETTER NAME

LUCY

  1. LUCY
  2. LCUY
  3. LCYU
  4. LUYC
  5. LYUC
  6. LYCU
  7. ULCY
  8. ULYC
  9. UCLY
  10. UCYL
  11. UYCL
  12. UYLC
  13. CYLU
  14. CYUL
  15. CUYL
  16. CULY
  17. CLUY
  18. CLYU
  19. YLCU
  20. YLUC
  21. YULC
  22. YUCL
  23. YCLU
  24. YCUL

I am now going to test this out on different names and see if I can find a pattern.

2 LETTER NAME

MO

1) MO

2) OM

3 LETTER NAME

JOE

1) JOE

2) JEO

3) EJO

4) EOJ

5) OEJ

6) OJE

5 LETTER NAME

RICKY

  1. RICKY
  2. RICYK                    
  3. RIKCY                    
  4. RIKYC                      
  5. RIYCK                    
  6. RIYKC                    
  7. RCIKY                    
  8. RCIYK                    
  9. RCYIK                    
  10. RCYKI                    
  11. RCKIY
  12. RCKYI            
  13. RKYCI
  14. RKYIC
  15. RKICY
  16. RKIYC
  17. RKCYI
  18. RKCIY
  19. RYICK
  20. RYIKC
  21. RYKCI
  22. RYKIC
  23. RYCKI
  24. RYCIK
  25. ICKYR
  26. ICKRY
  27. ICRYK
  28. ICRKY
  29. ICYRK
  30. ICYKR
  31. IKYCR
  32. IKYRC
  33. IKCYR
  34. IKCRY
  35. IKRCY
  36. IKRYC
  37. IYRKC
  38. IYRCK
  39. IYCRK
  40. IYCKR
  41. IYKRC
  42. IYKCR
  43. IRCKY
  44. IRCYK
  45. IRKCY
  46. IRKYC
  47. IRYCK
  48. IRYKC
  49. CKYRI
  50. CKYIR
  51. CKRIY
  52. CKRYI
  53. CKIRY
  54. CKIYR
  55. CYRIK
  56. CYRKI
  57. CYIRK
  58. CYIKR
  59. CYKRI
  60. CYKIR
  61. CRYKI
  62. CRYIK
  63. CRKYI
  64. CRKIY
  65. CRIKY
  66. CRIYK
  67. CIRKY
  68. CIRYK
  69. CIKYR
  70. CIKRY
  71. CIYKR
  72. CIYRK
  73. KYRIC
  74. KYRCI
  75. KYICR
  76. KYIRC
  77. KYCRI
  78. KYCIR
  79. KRCIY
  80. KRCYI
  81. KRIYC
  82. KRICY
  83. KRYIC
  84. KRYCI
  85. KICYR
  86. KICRY
  87. KIYCR
  88. KIYRC
  89. KIRYC
  90. KIRCY
  91. KCYIR
  92. KCYRI
  93. KCIYR
  94. KCIRY
  95. KCRYI
  96. KCRIY
  97. YRICK
  98. YRIKC
  99. YRCIK
  100. YRCKI
  101. YRKCI
  102. YRKIC
  103. YICKR
  104. YICRK
  105. YIKCR
  106. YIKRC
  107. YIRCK
  108. YIRKC
  109. YCKRI
  110. YCKIR
  111. YCRIK
  112. YCRKI
  113. YCIRK
  114. YCIKR
  115. YKRIC
  116. YKRCI
  117. YKIRC
  118. YKICR
  119. YKCRI
  120. YKCIR

Name

No. Of letters

No. Of permutations

MO

2

2

JOE

3

6

LUCY

4

24

RICKY

5

120

       I found that when you multiply the no. of letters by the previous amount of permutations, you will find the correct amount of permutations.

To find out how many permutations there are in a 3-letter word: 3*2 = 6 (which is 3!)

To find out how many permutations there are in a 4-letter word: 4*6= 24 (which is 4!)          

I also noticed that each no.

...read more.

Middle

NO. OF LETTERS IN NAME

NO. OF COMBINATIONS

1

1

2

2

3

6

4

24

Therefore,

NAME

NO. OF LETTERS

NO. OF PERMUTATIONS

TIM

3

6

FRED

4

24

CRAIG

5

120

CLARKE

6

720

CHARLIE

7

5040

CHARLTON

8

40320

I am now going to test weather duplicates of letters will make a difference in the no. of permutations.

3 LETTER NAME

WITH 2 LETTERS THE REPEATED

BOB

  1. BOB
  2. BBO
  3. OBB

4 LETTER NAME

WITH 2 LETTER THE REPEATED

EMMA

  1. EMMA
  2. EMAM
  3. EAMM
  4. MEMA
  5. MEAM
  6. MMEA
  7. MMAE
  8. MAME
  9. MAEM
  10. AEMM
  11. AMEM
  12. AMME

4 LETTER NAME

WITH 3 LETTERS THE REPEATED

LILL

  1. LILL
  2. ILLL
  3. LLIL
  4. LLLI

5 LETTER NAME

WITH 2 LETTERS THE REPEATED TWICE

EDDIE

  1. EDDIE
  2. EDDEI
  3. EDIDE
  4. EDIED
  5. EDEID
  6. EDEDI
  7. EIEDD
  8. EIDDE
  9. EIDED
  10. EEIDD
  11. EEDID
  12. EEDDI
  13. DDIEE
  14. DDEIE
  15. DDEEI
  16. DEDIE
  17. DEDEI
  18. DEIDE
  19. DEIED
  20. DIEED
  21. DIEDE
  22. DIDEE
  23. DEEID
  24. DEEDI
  25. IEEDD
  26. IDDEE
  27. IDEDE
  28. IDEED
  29. IEDED
  30. IEDDE

5 LETTER WORD WITH 3 LETTERS REPEATED

DADDY

  1. DADDY
  2. DDDAY
  3. DDDYA
  4. DDADY
  5. DDAYD
  6. DADYD
  7. ADDDY
  8. ADDYD
  9. ADYDD
  10. AYDDD
  11. YDDDA
  12. YDDAD
  13. YDADD
  14. YADDD
  15. DDYAD
  16. DDYDA
  17. DAYDD
  18. DYADD
  19. DYDAD
  20. DYDDA

NAME

NO. OF LETTERS

NO. OF REPEATED LETTERS

NO. OF PERMUTATIONS

BOB

3

2(B)

3

EMMA

4

2(M)

12

LILL

4

3(L)

4

EDDIE

5

2(E) + 2(D)

30

DADDY

5

3(D)

20


...read more.

Conclusion

N! , that no. of

                                                                                      X!

permutations was divided by 2 (which is 2!) to find the number of permutations.

For 5 letters with 2x’s & 3y’s after using the formula N!  , that no. of

                                                                                      X!

permutations was divided by 6 (which is 3!) to find the number of permutations

This shows another pattern of factorial.

Therefore you need to divide the formula by Y!. This now becomes:

N!

X! *Y!

Now using this formula I will be able to determine the no. Of permutations in any name or letter combination.

Using my formula I can prove how many permutations are in these names

NAME

NO. OF LETTERS

NO. OF PERMUTATIONS

ROBERT

6

360

RICHARD

7

2520

FREDDIE

7

1260

HARRISON

8

20160

THANCANAMOOTOO

14

151351200

Now I will find out the no. Of permutations using x’s & y’s

PERMUTATION

NO. OF LETTERS

NO. OF X’S

NO. OF Y’S

NO. OF PERMUTATIONS

XXYYYYY

7

2

5

21

XXXXXYYY

8

5

3

56

XXXXXXXXY

9

8

1

9

XXXXXYYYYY

10

5

5

252

XXXXXXXXXXX

YYYYYYYYY

20

11

9

167960

Page

...read more.

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