Calculators & Converters

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

    The 7 letters word ALGEBRA can be arranged in 2520 distinct ways. The below detailed information shows how to find how many ways are there to order the letters ALGEBRA and how it is being calculated in the real world problems.

    Enter word :       

    Distinguishable Ways to Arrange the Word ALGEBRA
    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 ALGEBRA be arranged.

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

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

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

    Distinct subsets:
    Subsets : A = 2; L = 1; G = 1; E = 1; B = 1; R = 1;
    Subsets' count:
    n1(A) = 2, n2(L) = 1, n3(G) = 1, n4(E) = 1, n5(B) = 1, n6(R) = 1

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

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

    = 5040/2

    = 2520
    nPr of word ALGEBRA = 2520

    Hence,
    The letters of the word ALGEBRA can be arranged in 2520 distinct ways.

    Apart from the word ALGEBRA, 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.

    getcalc.com Calculators