Emma's Dilemma - Statistics Experiment

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Emma's Dilemma - Statistics Experiment

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, 3 same, 4 arrangements

AAAA - 4 letter word, 4 same, 1 arrangements

KATIE, KATEI, KAEIT, KAETI, KAITE, KAIET, KTAIE, KTAEI, KTEIA, KTEAI,

KTIAE, KTIAE, KIAET, KIATE, KIETA, KIEAT, KITEA, KITAE, KEITA, KEIAT,

KEATI, KEAIT, KETIA, KETAI, AKTIE, AKTEI, AKEIT, AKETI, AKITE, AKIET,

ATKIE, ATKEI, ATEIK, ATEKI, ATIKE, ATIKE, AIAKT, AIKTE, AIETK, AIEKT,

AITEK, AITKE, AEITK, AEIKT, AEKTI, AEKIT, AETIK, AETKI, TAKIE, TAKEI,

TAEIK, TAEKI, TAIKE, TAIEK, TKAIE, TKAEI, TKEIA, TKEAI, TKIAE, TKIAE,

TIAEK, TIAKE, TIEKA, TIEAK, TIKEA, TIKAE, TEIKA, TEIAK, TEAKI, TEAIK,

TEKIA, TEKAI, IATKE, IATKI, IAEKT, IAETK, IAKTE, IAKET, ITAKE...

... middle of paper ...

... 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.

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