Emma's Dilemma

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Emma's Dilemma

For our maths coursework we had to investigate the number of different word arrangements possible for names. The names (or letter arrangements) I started off with had letters that were only used once n each name and were not repeated, like "Lucy". As I continued experimenting with the different arrangements, I began to use words with letters repeating, such as "Emma". My goal was to find formulas that worked for the different arrangements.

I started off by working out the number of different arrangements in the name "Emma". I shall now display the different arrangements of "Emma" that I found:

EMMA

EMAM

EAMM

MMEA

MMAE

MAME

MAEM

MEAM

MEMA

AMME

AEMM

AMEM

Here are the different letter arrangements for "Lucy":

LUCY ULCY CLUY YLUC

LUYC ULYC CLYU YLCU

LCUY UCLY CULY YULC

LCYU UCYL CUYL YUCL

LYUC UYLC CYLU YCLU

LYCU UYCL CYUL YCUL

I will now go through the different arrangements for names or word arrangements that do not have any repeats and are one, two, three, four and