What is the number of words formed using the letters of the word COMPUTER, so that all the vowels are always together?

Correct option is D

​$$\begin{aligned}&\textbf{Given word:} \quad \text{C O M P U T E R} \\[5pt]&\bullet\ \textbf{Vowels: } \text{O, U, E (3 vowels)} \\&\bullet\ \textbf{Consonants: } \text{C, M, P, T, R (5 consonants)} \\[10pt]&\textbf{Treat the Vowels as a Single Unit} \\[5pt]&\text{Since the vowels must always stay together, consider them as } \textbf{one combined unit.} \\[3pt]&\text{Units to arrange: } [\text{OUE}], \text{C, M, P, T, R (total of 6 units)} \\[10pt]&\textbf{Calculate the Arrangements of the Units} \\[3pt]&\text{The number of ways to arrange these 6 distinct units is:} \\&6! = 720 \\[10pt]&\textbf{Arrange the Vowels Within Their Unit} \\[3pt]&\text{The 3 vowels (O, U, E) can be arranged among themselves in:} \\&3! = 6\ \text{ways} \\[10pt]&\textbf{Multiply the Arrangements} \\[3pt]&\text{Total number of valid words = (Arrangements of units)} \times \text{(Arrangements of vowels within their unit):} \\&6! \times 3! = 720 \times 6 = {4320}\end{aligned}$$​​