# How Many Ways are There to Order the Letters of Word MATHEMATICS?

The 11 letters word MATHEMATICS can be arranged in 4989600 distinct ways. The below detailed information shows how to find how many ways are there to order the letters MATHEMATICS and how it is being calculated in the real world problems.

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Distinguishable Ways to Arrange the Word MATHEMATICS
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 MATHEMATICS be arranged.

Objective:
Find how many distinguishable ways are there to order the letters in the word MATHEMATICS.

Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters MATHEMATICS.
Formula:
nPr =n!/(n1! n2! . . . nr!)

Input parameters and values:
Total number of letters in MATHEMATICS:
n = 11

Distinct subsets:
Subsets : M = 2; A = 2; T = 2; H = 1; E = 1; I = 1; C = 1; S = 1;
Subsets' count:
n1(M) = 2, n2(A) = 2, n3(T) = 2, n4(H) = 1, n5(E) = 1, n6(I) = 1, n7(C) = 1, n8(S) = 1

step 2 Apply the values extracted from the word MATHEMATICS in the (nPr) permutations equation
nPr = 11!/(2! 2! 2! 1! 1! 1! 1! 1! )

= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11/{(1 x 2) (1 x 2) (1 x 2) (1) (1) (1) (1) (1)}

= 39916800/8

= 4989600
nPr of word MATHEMATICS = 4989600

Hence,
The letters of the word MATHEMATICS can be arranged in 4989600 distinct ways.

Apart from the word MATHEMATICS, 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.