Question

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

Answer 1

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=
`(12!)/(2!*2!*2!)= (12*11*10*9*8*7*6*5*4*3*2*1)/(2*1*2*1*2*1) =` = 59,875,200