Unique Ways to Arrange Alphabets of Word MANSION
The 7 letters word MANSION can be arranged in 2520 distinct ways. The below detailed information shows how to find how many ways are there to order the letters MANSION and how it is being arranged in the real world problems.
Possible Arrangements of Alphabets in "MANSION"
The 7 letters word MANSION can be arranged in 2520 unique ways. Below is the list of all possible unique arrangements:
Unique Ways to Arrange the Word MANSION
The below step by step work generated by this permutation calculator shows how to find how many different ways, the letters of the word MANSION can be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word MANSION.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters MANSION.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in MANSION:
n = 7
Distinct subsets:
Subsets : M = 1; A = 1; N = 2; S = 1; I = 1; O = 1;
Subsets' count:
n1(M) = 1, n2(A) = 1, n3(N) = 2, n4(S) = 1, n5(I) = 1, n6(O) = 1
step 2 Apply the values extracted from the word MANSION in the (nPr) permutations equation
nPr = 7!/(1! 1! 2! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5 x 6 x 7/{(1) (1) (1 x 2) (1) (1) (1)}
= 5040/2
= 2520
nPr of word MANSION = 2520
Hence,
The letters of the word MANSION can be arranged in 2520 distinct ways.
Apart from the word MANSION, 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.
