Calculators & Converters

    How many Ways to Arrange 13 Letters Word MASSACHUSETTS?

    64864800 is the number of ways to arrange 13 letters (alphabets) word "MASSACHUSETTS" by using Permutations (nPr) formula. Users may refer the below workout with step by step procedure to understand how to estimate how many number of ways to arrange 13 alphabets or letters of a "MASSACHUSETTS". The partial possible number of ways to arrange the letters of word "MASSACHUSETTS" are CTMSHSATESSUA, TSAUSCTSEASHM, HSCEASUASTMTS, ACTUSSHMETASS, SUSCHEAMSTTSA, CSSTSAAMTHUES, ATSHSACUETSSM, SUASESCSTMTAH, CTSASSUSTEAMH, MSSSTEATAUHCS. Refresh the page to get the another set of partial arrangements.

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    Distinct Ways to Arrange Word MASSACHUSETTS - Workout


    The below workout is the step by step procedure to find how many number of distinct ways to arrange the 13 letters (alphabets) of word "MASSACHUSETTS". Users may use any other word by changing the word "MASSACHUSETTS" to find the total number of distinct ways to arrange different words.

    Step by step workout
    step 1 Address the formula, input parameters and values
    Formula:
    nPr =n!/(n1! n2! . . . nk!)
    Input Parameters & Values:
    Total number of alphabets (n) & subsets (n1, n2, . . nk) in the word "MASSACHUSETTS"
    n = 13
    Subsets : M = 1; A = 2; S = 4; C = 1; H = 1; U = 1; E = 1; T = 2;
    n1(M) = 1, n2(A) = 2, n3(S) = 4, n4(C) = 1, n5(H) = 1, n6(U) = 1, n7(E) = 1, n8(T) = 2

    step 2 Apply the input parameter values in the nPr formula
    = 13!/(1! 2! 4! 1! 1! 1! 1! 2! )

    = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13/{(1) (1 x 2) (1 x 2 x 3 x 4) (1) (1) (1) (1) (1 x 2)}

    = 6227020800/96

    = 64864800

    In 64864800 distinct ways, the letters of word "MASSACHUSETTS" can be arranged.

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