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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,...

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