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Emma's dilemma. 1] Below are the different permutations for the letters in the name Emma, EMMA MMAE MAME AMME EMAM MMEA MEAM AMEM EAMM MEMA MAEM AEMM There are 12 different permutations altogether for the letters in the name Emma. There is this amount of permutations s for all four letter names with two of the letters the same. 2] Below are the different permutations for the letters in the name Lucy, LUCY ULCY CULY YCUL LUYC ULYC CUYL YCLU LCUY UCYL CYUL YUCL LCYU UCLY CYLU YULC LYUC UYLC CLUY YLUC LYCU UYCL CLYU YLCU There are 24 permutations for the letters in the name Lucy, twice the amount there is for Emma. 3] 1st I have decided to investigate names without any letters that are the same In a one letter name there is only one permutation, X In a two-letter name with all the letters different there are two permutations, XY YX In a three-letter name with all the letters different, e.g. Tim, there are six permutations, TIM ITM MIT TMI IMT MTI In a four-letter name (like Lucy Shown above) there are 24 different arrangements, LUCY ULCY CULY YCUL LUYC ULYC CUYL YCLU LCUY UCYL CYUL YUCL LCYU UCLY CYLU YULC LYUC UYLC CLUY YLUC LYCU UYCL CLYU YLCU No' of letters 1 2 3 4 5 No' of arrangements 1 2 5 24 120 The answer for the five-lettered name is predicted, I got this result...

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