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, ITAEK, ITEKA, ITEAK, ITKAE, ITKAE, IKAET, IKATE, IKETA, IKEAT, IKTEA, IKTAE, IEKTA, IEKAT, IEATK, IEAKT, IETKA, IETAK, EATIK, EATKI, EAKIT, EAKTI, EAITK, EAIKT, ETAIK, ETAKI, ETKIA, ETKAI, ETIAK, ETIAK, EIAKT, EIATK, EIKTA, EIKAT, EITKA, EITAK, EKITA, EKIAT, EKATI, EKAIT, EKTIA, EKTAI, - 5 letter word, 0 same, 120 arrangements
GEMMA, GEMAM, GEAMM, GAEMM, GAMEM, GAMME, GMMEA, GMMAE, GMAEM, GMEMA, GMEAM, GMAME, EMMAG, EMMGA, EMGAM, EMGMA, EMAGM, EMAMG, EAMMG, EAMGM, EAGMM, EGMMA, EGMAM, EGAMM, AMMEG, AMMGE, AMGEM, AMGME, AMEGM, AMEMG, AEMMG, AEMGM, AEGMM, AGMME, AGMEM, AGEMM, 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
To find out the possible number of arrangements of a word
Number of arrangements = χ!
If the word has 2 letters the same
Number of arrangements = χ! ÷ 2!
The original figure must be divided because when multiply letters are the same they act as one and cut down the possible number of arrangements.
For example
ABC, ACB, BAC, BCA, CBA, CAB,
But if the C is replaced with an a
ABA, AAB, BAA, BAA, ABA, AAB,
We find that the arrangements are repeated,.
To find the number of arrangements for a word, first of all the letters must be counted.
E.g. Mississippi, has 11 letters
Then the different letters it has
E.G. Mississippi
There is M, I, S, & P
Then the amount of each on these letters must be counted
M = 1
I = 4
S = 4
P = 2
Since the word has 11 letters
1 × 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
