Calculators & Converters

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

    The 7 letters word FLORIDA can be arranged in 5040 distinct ways. The below detailed information shows how to find how many ways are there to order the letters FLORIDA and how it is being calculated in the real world problems.

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    Distinguishable Ways to Arrange the Word FLORIDA
    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 FLORIDA be arranged.

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

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

    Input parameters and values:
    Total number of letters in FLORIDA:
    n = 7

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

    step 2 Apply the values extracted from the word FLORIDA in the (nPr) permutations equation
    nPr = 7!/(1! 1! 1! 1! 1! 1! 1! )

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

    = 5040/1

    = 5040
    nPr of word FLORIDA = 5040

    Hence,
    The letters of the word FLORIDA can be arranged in 5040 distinct ways.

    Apart from the word FLORIDA, 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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