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Emma's Dilemma  

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Mathematics GCSE coursework: Emma's Dilemma In my investigation I am going to investigate the number of possible arrangements of the letters in peoples names. I start with the least possible amount of letters, which is one: J This clearly only has one arrangement. I will now go on to investigate the number of arrangements of letters in names going up in order of the number of letters that they contain: AL LA (2 arrangements) SAM SMA ASM AMS MSA MAS (6 arrangements) LUCY LCUY LCYU LUYC LYCU LYUC ULYC ULCY UCLY UCYL UYCL UYLC CLUY CLYU CUYL CULY CYLU CUUL YLUC YLCU YULC YUCL YCUL YCLU (24 arrangements) I can see that if the name has no letters that are repeated I can work out the number of different possibilities more easily. I have worked out that when I have exhausted the different number of possible combinations starting with the same letter I can times that by the number of letters in the word to work out the number of formulas. For example, when doing the name Lucy I can cut down the time it would take to...

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