How Many Ways are There to Order the Letters 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 calculated in the real world problems.
Distinguishable Ways to Arrange the Word LONDON
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 LONDON 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.
