In how many ways can the letters of the word 'DAUGHTER' be arranged so that the vowels always come together?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4320
To keep the vowels together, tie them into one block, arrange the block with the other letters, and then arrange the vowels inside the block.
DAUGHTER has 8 different letters; its vowels are A, U and E.
The block (AUE) with D, G, H, T, R makes 6 units: \(6!=720\) arrangements
The 3 vowels inside the block: \(3!=6\) arrangements
Total \(=720\times6=4320\)