How many words can be formed from the letters of the word IMAGINARY so that the vowels never come together?

The Word "IMAGINARY" has 9 letters, including 4 vowels (I, A, I, A) and 5 consonants (M, G, N, R, Y). To find the number of arrangements where the vowels do not come together, first calculate the total arrangements of the letters (considering the repeated vowels) and then subtract the arrangements where the vowels are together, treating them as a single unit. After performing these calculations, the total number of arrangements where the vowels never come together is found to be 2880.