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The number of possible different 12-letter arrangements of the letters in the word “TRIGONOMETRY” is represented by

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HomertheGenius

We will use formula for Permutations with repetition:
P(n, m1,m2,m3) = n! / m1! · m2! · m3!
In the word TRIGONOMETRY we have repetitions of letters: T, R and O.
P=\(\frac{12!}{2!*2!*2!}= \frac{12*11*10*9*8*7*6*5*4*3*2*1}{2*1*2*1*2*1} =\) = 59,875,200 

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