How many words can be formed from the letters of the word "PRODUCER" so that the vowels are always together?

PRODUCER has 8 letters with vowels O, U, E (3 vowels) and consonants P, R, D, C, R (5 consonants). Treat the 3 vowels as one unit. We have 6 units total (5 consonants + 1 vowel group). These can be arranged in 6! ways = 720. Within the vowel group, 3 vowels can be arranged in 3! ways = 6. Total arrangements = 720 × 6 = 4320. But wait, PRODUCER has two Rs. We need to account for this. Consonants are P, R, D, C, R - with R repeated. Arrangements of consonants = 5!/2! = 60. Total = 60 × 6 × 6 = 2160. This matches option B.