In how many ways are the letters of the word DOCUMENT arranged so that all the vowels always come together?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4320
To keep some letters together, tie them into one block: arrange the block with the other letters, then arrange the letters inside the block. DOCUMENT has 8 different letters; its vowels are O, U and E.
The block (OUE) and the 5 consonants D, C, M, N, T make 6 units, which can be arranged in \(6!=720\) ways
The 3 vowels can be arranged inside the block in \(3!=6\) ways
Number of ways \(=720\times6=4320\)