Unique Ways to Arrange Alphabets of Word LONDON
The 6 letters word LONDON can be arranged in 180 distinct ways. The below detailed information shows how to find how many ways are there to order the letters LONDON and how it is being arranged in the real world problems.
Possible Arrangements of Alphabets in "LONDON"
The 6 letters word LONDON can be arranged in 180 unique ways. Below is the list of all possible unique arrangements:
Unique Ways to Arrange the Word LONDON
The below step by step work generated by this permutation calculator shows how to find how many different ways, the letters of the word LONDON can be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word LONDON.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters LONDON.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in LONDON:
n = 6
Distinct subsets:
Subsets : L = 1; O = 2; N = 2; D = 1;
Subsets' count:
n1(L) = 1, n2(O) = 2, n3(N) = 2, n4(D) = 1
step 2 Apply the values extracted from the word LONDON in the (nPr) permutations equation
nPr = 6!/(1! 2! 2! 1! )
= 1 x 2 x 3 x 4 x 5 x 6/{(1) (1 x 2) (1 x 2) (1)}
= 720/4
= 180
nPr of word LONDON = 180
Hence,
The letters of the word LONDON can be arranged in 180 distinct ways.
Apart from the word LONDON, 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.
