How Many Ways are There to Order the Letters of Word DOMAIN?
The 6 letters word DOMAIN can be arranged in 720 distinct ways. The below detailed information shows how to find how many ways are there to order the letters DOMAIN and how it is being calculated in the real world problems.
Distinguishable Ways to Arrange the Word DOMAIN
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 DOMAIN be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word DOMAIN.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters DOMAIN.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in DOMAIN:
n = 6
Distinct subsets:
Subsets : D = 1; O = 1; M = 1; A = 1; I = 1; N = 1;
Subsets' count:
n1(D) = 1, n2(O) = 1, n3(M) = 1, n4(A) = 1, n5(I) = 1, n6(N) = 1
step 2 Apply the values extracted from the word DOMAIN in the (nPr) permutations equation
nPr = 6!/(1! 1! 1! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5 x 6/{(1) (1) (1) (1) (1) (1)}
= 720/1
= 720
nPr of word DOMAIN = 720
Hence,
The letters of the word DOMAIN can be arranged in 720 distinct ways.
Apart from the word DOMAIN, 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.
