How Many Ways are There to Order the Letters of Word MONTANA?
The 7 letters word MONTANA can be arranged in 1260 distinct ways. The below detailed information shows how to find how many ways are there to order the letters MONTANA and how it is being calculated in the real world problems.
Distinguishable Ways to Arrange the Word MONTANA
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 MONTANA be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word MONTANA.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters MONTANA.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in MONTANA:
n = 7
Distinct subsets:
Subsets : M = 1; O = 1; N = 2; T = 1; A = 2;
Subsets' count:
n1(M) = 1, n2(O) = 1, n3(N) = 2, n4(T) = 1, n5(A) = 2
step 2 Apply the values extracted from the word MONTANA in the (nPr) permutations equation
nPr = 7!/(1! 1! 2! 1! 2! )
= 1 x 2 x 3 x 4 x 5 x 6 x 7/{(1) (1) (1 x 2) (1) (1 x 2)}
= 5040/4
= 1260
nPr of word MONTANA = 1260
Hence,
The letters of the word MONTANA can be arranged in 1260 distinct ways.
Apart from the word MONTANA, 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.
