Unique Ways to Arrange Alphabets of Word MOUTH
The 5 letters word MOUTH can be arranged in 120 distinct ways. The below detailed information shows how to find how many ways are there to order the letters MOUTH and how it is being arranged in the real world problems.
Possible Arrangements of Alphabets in "MOUTH"
The 5 letters word MOUTH can be arranged in 120 unique ways. Below is the list of all possible unique arrangements:
Unique Ways to Arrange the Word MOUTH
The below step by step work generated by this permutation calculator shows how to find how many different ways, the letters of the word MOUTH can be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word MOUTH.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters MOUTH.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in MOUTH:
n = 5
Distinct subsets:
Subsets : M = 1; O = 1; U = 1; T = 1; H = 1;
Subsets' count:
n1(M) = 1, n2(O) = 1, n3(U) = 1, n4(T) = 1, n5(H) = 1
step 2 Apply the values extracted from the word MOUTH in the (nPr) permutations equation
nPr = 5!/(1! 1! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5/{(1) (1) (1) (1) (1)}
= 120/1
= 120
nPr of word MOUTH = 120
Hence,
The letters of the word MOUTH can be arranged in 120 distinct ways.
Apart from the word MOUTH, 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.
