In how many different ways can the letters of the word BANKING be arranged in such a way that the vowels always come together?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 720
To keep the vowels together, they are tied into one block: the block is arranged with the other letters, and then the vowels are arranged inside the block. BANKING has 7 letters, with N twice; its vowels are A and I.
Units to arrange: (AI), B, N, K, N, G — 6 units, with N repeated
Arrangements of the units: \(\displaystyle\frac{6!}{2!}=\frac{720}{2}=360\)
A and I can stand inside the block in \(2!=2\) ways
Total: \(360\times2=720\)