In how may different ways can the letters of the word EXTRA be arranged so that the vowels are never come together?

The word 'EXTRA' contains 5 different letters.
The word EXTRA can be arranged in 5! ways = 120 ways

When the vowels EA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters XTR(EA).
Now, 4 letters can be arranged in 4! ways
= 24 ways.
The vowels (EA) can be arranged among themselves in 2! = 2 ways.
∴ The word EXTRA can be arranged in such a way that the vowels will be together = (24 x 2) =48


The letters of the words EXTRA be arranged so that the vowels are never together = (120 - 48) = 72 ways.