answer :

Distinct Ways to Arrange Word LIATAKUNDIWEB - 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 "LIATAKUNDIWEB". Users may use any other word by changing the word "LIATAKUNDIWEB" 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 "LIATAKUNDIWEB"

n = 13

Subsets : L = 1; I = 2; A = 2; T = 1; K = 1; U = 1; N = 1; D = 1; W = 1; E = 1; B = 1;

n1(L) = 1, n2(I) = 2, n3(A) = 2, n4(T) = 1, n5(K) = 1, n6(U) = 1, n7(N) = 1, n8(D) = 1, n9(W) = 1, n10(E) = 1, n11(B) = 1

step 2

Apply the input parameter values in the nPr formula

=13!  / (1! 2! 2! 1! 1! 1! 1! 1! 1! 1! 1! )

=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) (1) (1) (1) (1) (1) (1) (1) (1)}

=6227020800  / 4

= 1556755200

In 1556755200 distinct ways, the letters of word "LIATAKUNDIWEB" can be arranged.

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