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GCSE Mathematics Coursework - Emma's Dilemma Method: First, I tested different arrangements of the name 'EMMA', by systematically rearranging the letters in the name such as: 1-EMMA 4-AEMM 7-MMEA 10-MEAM 2-EAMM 5-AMME 8-MEMA 11-MAEM 3-EMAM 6-AMEM 9-MMAE 12-MAME I found that there were twelve arrangements for the name 'EMMA'. I then investigated different arrangements of letters in the name 'LUCY', using the same method: 1-LUCY 7-UCYL 13-CYLU 19-YCLU 2-LUYC 8-UCLY 14-CYUL 20-YCUL 3-LCUY 9-UYLC 15-CUYL 21-YUCL 4-LCYU 10-UYCL 16-CULY 22-YULC 5-LYCU 11-ULCY 17-CLYU 23-YLCU 6-LYUC 12-ULYC 18-CLUY 24-YLUC I found that there were many more arrangements in the name 'LUCY' than in the name 'EMMA'. This is because the name 'EMMA' contains repeated letters and the name 'LUCY' does not. I then investigated how many different arrangements of letters there were in other names of different lengths. The lengths of names that I used were 2, 3, and 4 letter names. I recorded my results in a table. Table showing the number of different arrangements of letters possible in words of different lengths with no repeated letters Number of letters Number of different arrangements 1 1 2 2 3 6 4 24 After recording the...

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