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

720

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

6!2!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