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Emma's Dilemma.

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Introduction

EMMA, EMAM, EAMM, AEMM, AMEM, AMME, MMEA, MMAE, MAEM, MEMA, MEAM, MAME. - There is 12 ways to arrange the word Emma. LUCY, LUYC, LYCU, LYUC, LCUY, LCYU, YUCL, YULC, YCLU, YCUL, YLUC, YLCU, CLYU, CLUY, CULY, CUYL, CYUL, CYLU, UCLY, UCYL, ULCY, ULYC, UYLC, UYCL - There is 24 ways to arrange the word Lucy. A, - 1 letter word, 1 Arrangement TO, OT - 2 letter word, 0 same, 2 arrangements AA - 2 letter word, 2 same, 1 arrangements AMY, AYM, YMA, YAM, MAY, MYA - 3 letter word, 0 same, 6 arrangements AAB, ABA, BAA - 3 letter word, 2 same, 3 arrangements AAA - 3 letter word, 3 same, 1 arrangements KATE, KAET, KTEA, KTAE, KEAT, KETA, TEAK, TEKA, TAKE, TAEK, TKEA, TAKE, EAKT, EATK, ETKA, ETAK, EKTA, EKAT, AEKT, AETK, AKTE, AKET, ATEK, ATKE - 4 letter word, 0 same, 24 arrangements EMMA, EMAM, EAMM, AEMM, AMEM, AMME, MMEA, MMAE, MAEM, MEMA, MEAM, MAME - 4 letter word, 0 same, 12 arrangements AAAB, AABA, ABAA, BAAA - 4 letter word, ...read more.

Middle

MMAEG, MMAGE, MMEGA, MMEAG, MMGAE, MMGEA, MAMGE, MAMEG, MAGEM, MAGME, MAEMG, MAEGM, MEAGM, MEAMG, MEMAG, MEMGA, MEGMA, MEGAM, MGAEM, MGAME, MGEAM, MGEMA, MGMAE, MGMEA - 5 letter word, 2 same, 60 arrangements AAABC, AAACB, AACBA, AACAB, AABCA, AABAC, ABAAC, ABACA, ABCAA, ACBAA, ACABA, ACAAB, BAAAC, BAACA, BACAA, BCAAA, CBAAA, CABAA, CAABA, CAAAB - 5 letter word, 3 same, 20 arrangements 0 same 2 same 3 same 4 same 5 same 6 same 7 same 8 same 9 same 10 same 1 letter 1 - - - - - - - - - 2 letters 2 1 - - - - - - - - 3 letters 6 3 1 - - - - - - - 4 letters 24 12 4 1 - - - - - - 5 letters 120 60 20 5 1 - - - - - 6 letters 720 360 120 30 6 1 - - - - 7 letters 5040 2520 840 210 42 7 1 - - - 8 letters 40320 20160 6720 1680 336 56 8 1 - - 9 ...read more.

Conclusion

� 2 � 3 � 4 � 5 � 6 � 7 � 8 � 9 � 10 � 11 = 11! = 39916800 Mississippi has 4 of 1 letter, 4 of another letter, 2 of another and 1 of another. Since with letters of the same there is less combinations so to work this out we: 39916800 � 4! � 4! �2! �1! = 34650, Mississippi has this many arrangements Antidisestablishmentareanism there is a total of 28 letters, A = 4 N = 3 T = 3 I = 4 D = 1 S = 4 E = 3 B = 1 L = 1 H = 1 M = 2 28! = 304888344611713860501504000000 304888344611713860501504000000 � 4! � 3! � 3! � 4! � 1! � 4! � 3! � 1! � 1! � 1! � 2 = 51053244861947328000000 = fifty one thousand trillion, five hundred and thirty two trillion, two hundred and forty four thousand billion, eight hundred and sixty one billion, nine hundred and forty seven thousand million, three hundred and twenty eight million ...read more.

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