Calculators & Converters

    How Many Ways are There to Order the Letters of Word CALIFORNIA?

    The 10 letters word CALIFORNIA can be arranged in 907200 distinct ways. The below detailed information shows how to find how many ways are there to order the letters CALIFORNIA and how it is being calculated in the real world problems.

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    Distinguishable Ways to Arrange the Word CALIFORNIA
    The below step by step work generated by the word permutations calculator shows how to find how many different ways can the letters of the word CALIFORNIA be arranged.

    Objective:
    Find how many distinguishable ways are there to order the letters in the word CALIFORNIA.

    Step by step workout:
    step 1 Address the formula, input parameters and values to find how many ways are there to order the letters CALIFORNIA.
    Formula:
    nPr =n!/(n1! n2! . . . nr!)

    Input parameters and values:
    Total number of letters in CALIFORNIA:
    n = 10

    Distinct subsets:
    Subsets : C = 1; A = 2; L = 1; I = 2; F = 1; O = 1; R = 1; N = 1;
    Subsets' count:
    n1(C) = 1, n2(A) = 2, n3(L) = 1, n4(I) = 2, n5(F) = 1, n6(O) = 1, n7(R) = 1, n8(N) = 1

    step 2 Apply the values extracted from the word CALIFORNIA in the (nPr) permutations equation
    nPr = 10!/(1! 2! 1! 2! 1! 1! 1! 1! )

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

    = 3628800/4

    = 907200
    nPr of word CALIFORNIA = 907200

    Hence,
    The letters of the word CALIFORNIA can be arranged in 907200 distinct ways.

    Apart from the word CALIFORNIA, you may try different words with various lengths with or without repetition of letters to observe how it affects the nPr word permutation calculation to find how many ways the letters in the given word can be arranged.

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