Unique Ways to Arrange Alphabets of Word MASSACHUSETTS
The 13 letters word MASSACHUSETTS can be arranged in 64864800 distinct ways. The below detailed information shows how to find how many ways are there to order the letters MASSACHUSETTS and how it is being arranged in the real world problems.
Unique Ways to Arrange the Word MASSACHUSETTS
The below step by step work generated by this permutation calculator shows how to find how many different ways, the letters of the word MASSACHUSETTS can be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word MASSACHUSETTS.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters MASSACHUSETTS.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in MASSACHUSETTS:
n = 13
Distinct subsets:
Subsets : M = 1; A = 2; S = 4; C = 1; H = 1; U = 1; E = 1; T = 2;
Subsets' count:
n1(M) = 1, n2(A) = 2, n3(S) = 4, n4(C) = 1, n5(H) = 1, n6(U) = 1, n7(E) = 1, n8(T) = 2
step 2 Apply the values extracted from the word MASSACHUSETTS in the (nPr) permutations equation
nPr = 13!/(1! 2! 4! 1! 1! 1! 1! 2! )
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13/{(1) (1 x 2) (1 x 2 x 3 x 4) (1) (1) (1) (1) (1 x 2)}
= 6227020800/96
= 64864800
nPr of word MASSACHUSETTS = 64864800
Hence,
The letters of the word MASSACHUSETTS can be arranged in 64864800 distinct ways.
Apart from the word MASSACHUSETTS, 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.
