The number of words that can be formed with the letters of the word 'DEFINITE' if two vowels are together and the other two are also together but separated from the first two is

Step-by-step solution

DEFINITE has 8 letters: Consonants: D, F, N, T (4 distinct); Vowels: E, E, I, I (4 letters with repetition). The condition requires two groups of 2 vowels each, separated by at least one consonant. Arrange 4 consonants: 4! = 24 ways, creating 5 gaps: _C _C _C _C _ Choose 2 gaps (separated) for the two vowel groups: 5 2 = 10 ways Arrange 4 vowels (E, E, I, I) in the 4 slots: 4! 2! 2! = 24 4 = 6 ways Total = 24 10 6 = 1440