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Emma's Dilemma First I am going to investigate how many different arrangements in the name LUCY, which has no letters the same. LUCY LUYC LYCU LYUC LCYU LCUY ULCY UCLY UYLC UYCL YCUL YUCL YULC YLCU YLUC CYLU CYUL CUYL CULY CLUY ULYC UCYL There are 4 different letters and there are 24different arrangements. SAM SMA MSA MAS ASM AMS There are 3 different letters in this name and 6 different arrangements. JO OJ There are 2 different letters in this name and there are 2 different arrangements. Table of Results Number of Letters Number of Different Arrangements 2 2 3 6 4 24 5 120 6 720 7 5040 From the table of results I have found out that a 2-letter word has 2 arrangements, and a 3-letter word has 6. Taking for example a 3 letter word, I have worked out that if we do 3 (the length of the word) x 2 = 6, the number of different arrangements. In a 4 letter word, to work out the amount of different arrangements you can do 4 x...

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