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  • Level: GCSE
  • Subject: Maths
  • Word count: 1424

Investigate the number of different arrangements of the letters in a name.

Extracts from this document...

Introduction

                                                                                                                                     Page 1

Emma’s Dilemma

Emma is playing around with arrangements of the letters of her name.

One arrangement is EMMA, a different arrangement is MEAM. Another arrangement is AEMM.

  1. Investigate the number of different arrangements of the letters of Emma’s name.

1. EMMA

2. AEMM

3. MAEM

4. MMAE

5. MMEA

6. AMME        12 WAYS

7. EAMM

8. MEAM

9. MEMA

10. AMEM

11. MAME

12. EMAM

Emma has a friend called Lucy.

  1. Investigate the number of different arrangements of the letters of Lucy’s name.

1. LUCY

2.YLUC

3. CYLU

4. UCYL

5. UCLY

6. YUCL      

7. LYUC

8. CLYU

9. CLUY

10. YCLU

11. UYCL

12. LUYC

13. ULYC

14. CULY

15. YCUL

                                                                                                                         Page 2

16. LYCU      24 WAYS

17. YLCU

18. UYLC

19. CUYL

20. LCUY

21. LCYU

22. ULCY

23. YULC

24. CYUL

Choose some different names.

  1. Investigate the number of different arrangements of the letters of the names you have chosen.

These names all have all letters different:

                                                                 1.Jo

                                                                 2.Max

                                                                 3.Mark

                                                                 4.James

  1. JO    2 WAYS
  2. OJ
  1. MAX
  2. XMA
...read more.

Middle

MSAJEEMSAJJEMSAAJEMSAJESMMAJESSMAJEESMAJJESMAJSEMAAJSEMMAJSEEMAJSSEMAJSEMJAASEMJJASEMMJASEEMJASMEJASSMEJAASMEJJASMEEJASMJMASEEJMASSEJMAASEJMMASEJMASJEEMASJJEMASSJEMAASJEMASJMEEASJMMEASJ

                                                                                                          Page 6

  1. JMEAS
  2. SJMEA
  3. SJMAE
  4. ESJMA
  5. AESJM
  6. MAESJ
  7. JMAES
  8. JAMSE
  9. EJAMS
  10. SEJAM
  11. MSEJA
  12. AMSEJ

      120.          MAJES

These names all have two letters the same:

                                                                    1.JJ

                                                                    2.BOB

                                                                    3.SAMM

                                                                    4. SARAH

  1. JJ         1 WAY
  1. BOB
  2. BBO    3 WAYS
  3. OBB
  1. SAMM
  2. MSAM
  3. MMSA
  4. AMMS
  5. AMSM
  6. MAMS       12 WAYS
  7. SMAM
  8. MSMA
  9. SMMA
  10. ASMM
  11. MASM
  12. MMAS

                                                                                                                      Page 7

  1. SARAH
  2. HSARA
  3. AHSAR
  4. RAHSA
  5. ARAHS
  6. ARASH
  7. HARAS
  8. SHARA
  9. ASHAR
  10. RASHA
  11. RASAH
  12. HRASA
  13. AHRAS
  14. SAHRA
  15. ASAHR
  16. ASARH
  17. HASAR
  18. RHASA
  19. ARHAS
  20. SARHA
  21. ASRHA
  22. AASRH
  23. HAASR
  24. RHAAS
  25. SRHAA
  26. RSHAA
  27. ARSHA
  28. AARSH
  29. HAARS
  30. SHAAR
  31. SHARA
  32. ASHAR
  33. RASHA
  34. ARASH
  35. HARAS
  36. HARSA
  37. AHARS
  38. SAHAR
  39. RSAHA
  40. ARSAH
  41. ASRHA
  42. AASRH

                                                                                                                  Page 8

  1. HAASR
  2. RHAAS
  3. SRHAA
  4. SHRAA   6O WAYS
  5. ASHRA
  6. AASHR
  7. RAASH
  8. HRAAS
  9. HRAAS
  10. SHRAA
  11. ASHRA
  12. AASHR
  13. RAASH
  14. RAAHS
  15. SRAAH
  16. HSRAA
  17. AHSRA
  18. AAHSR

These names all have three letters the same:

                                                                      1.

                                                                      2.

...read more.

Conclusion

                         6

Using this method I am able to predict the amount of different ways there are for names that haven’t got all letters the same. For example if I wanted to find the number of ways for a six letter word with two letters the same I would do 6!

                                                                                                                      2!

So it would be 6 (6-1) (6-2) (6-3) (6-4) (6-5)  which is 6 x 5 x 4 x 3 x 2 x 1

                                        2 (2-1)                                               2 x 1

So it would be 720. The number of ways for a six letter word with two letters the same would be 360. Another prediction would be if N = 7 and D = 3 I would place them in the formula so it would be 7!  Which is 7 (7-1) (7-2) (7-3) (7-4) (7-5) (7-6)

                                                        3!                               (3-1) (3-2)

So it would be 5040  so the number of ways for a seven letter word with three

                          6

letters the same would be 840.

In conclusion using the formulas N! and N! make it easier to find the number of different ways of arrangements in a word.

...read more.

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