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Mathan Navaratnam 11F 24.10.2001 Mathematics Coursework Emma's Dilemma The different arrangements for the name Emma are as follows: Emma emam eamm mmae Mmea meam mema mame Maem amme amem aemm There were a total of twelve combinations of the rearrangement of the name Emma. The name Emma consists of four letters where three of them being different, the two like letters being m. Emma's friend however, Lucy, name consists again of four letters but this time all the letters are different. The number of arrangements for the name Lucy is as follows: Lucy ucyl cylu ycul Luyc ucly cyul yclu Lcuy ulcy culy yulc Lcyu ulyc cuyl yucl Lyuc uycl clyu ylcu Lycu uylc cluy yluc This time there were twenty-four different possibilities in rearranging the name Lucy. This is significant, as it is exactly double the number of arrangements of the name Emma where there were 4 letters but where only 3 were different. Looking back at the table above I think it would be useful...

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