In how many different ways can the letters of the word BANKING be arranged in such a way that the vowels always come together?

Solution (By Examveda Team)

The given words contains 7 letters of which N is taken 2 times.
We keep the vowels (AI) together and treat them as 1 letter.
Thus, we have to arrange 6 letters BNKNG (AI) of which N occurs 2 times and rest are different.
These can be arranged in
$$\frac{6!}{2!}$$ = (6 × 5 × 4 × 3 ) = 360 days
Now 2 vowels (AI) can be arranged among themselves in 2 ways.
∴ Required number of ways = (360 × 2) = 720