In how many different ways can the letters of the word 'BANKING' be arranged so that the vowels always come together?

Question: In how many different ways can the letters of the word 'BANKING' be arranged so that the vowels always come together?

Solution:
In the word 'BANKING' we treat the two vowels 'A' and 'I' as one letter.
Thus, we have BNKNG(AI)

This has 6 letters of which N occurs 2 times and the rest are different.
As we know that number of ways of arranging n letters out of which r are of same type = n!/r!
Number of ways of arranging these letters = 6!/2! = 360

Now 2 vowels (A,l) can be arranged in 2! = 2 ways

∴ Required number of ways = 360 × 2 = 720