How many words can be formed by using the letters from the word 'DRIVER' such that all the vowels are never together?

Question: How many words can be formed by using the letters from the word 'DRIVER' such that all the vowels are never together?

Solution:
We assume all the vowels to be a single character, i.e., 'IE' is a single character.
So, now we have 5 characters in the word, namely, D, R, V, R, and IE.

But, R occurs 2 times.
Number of possible arrangements = 5!/2! = 60

Now,
​the two vowels can be arranged in 2! = 2 ways.

Total number of possible words such that the vowels are always together = 60 × 2 = 120

Total number of possible words = 6!/2! = 720/2 = 360

Therefore, the total number of possible words such that the vowels are never together = 360 - 120 = 240