Unique Ways to Arrange Alphabets of Word AUSTRALIA
The 9 letters word AUSTRALIA can be arranged in 60480 distinct ways. The below detailed information shows how to find how many ways are there to order the letters AUSTRALIA and how it is being arranged in the real world problems.
Unique Ways to Arrange the Word AUSTRALIA
The below step by step work generated by this permutation calculator shows how to find how many different ways, the letters of the word AUSTRALIA can be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word AUSTRALIA.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters AUSTRALIA.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in AUSTRALIA:
n = 9
Distinct subsets:
Subsets : A = 3; U = 1; S = 1; T = 1; R = 1; L = 1; I = 1;
Subsets' count:
n1(A) = 3, n2(U) = 1, n3(S) = 1, n4(T) = 1, n5(R) = 1, n6(L) = 1, n7(I) = 1
step 2 Apply the values extracted from the word AUSTRALIA in the (nPr) permutations equation
nPr = 9!/(3! 1! 1! 1! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9/{(1 x 2 x 3) (1) (1) (1) (1) (1) (1)}
= 362880/6
= 60480
nPr of word AUSTRALIA = 60480
Hence,
The letters of the word AUSTRALIA can be arranged in 60480 distinct ways.
Apart from the word AUSTRALIA, 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.
