Question

How many words with or without meaning, can be formed using the letters of the word ALLAHABAD so that vowels are never together

Answer 1

The word ALLAHABAD has 9 letters.
So the total number of arrangement is 9!/ (4! 2!)

And lets combine all the vowels to form a single alphabet, as 4 A's are there.
So together there are 6 letters.
So the arrangement = 6!/(2!)

So the arrangement without vowels together = total arrangement - vowels together
= 9!/ (4! 2!) - 6!/(2!)