‘EXTRA’ The given word contains 5 different letters Taking the vowels together, we treat them as on letter Then, the letters to be arranged are XTR (EA) These letters can be arranged in ∠4 = 4 . 3 . 2 . 1 = 24 ways The vowels EA may be arranged amongst themselves in ∠2 = 2 ways Number of words, each having vowels together = 24 × 2 = 48 Total number of words formed by using all the letters of the given words = ∠5 = 5 . 4 . 3 . 2 . 1 = 120 Hence, number of words, each having vowels never together = 120 – 48 = 72.