How many different arrangements of the letters of the word 'STRIVE' can be made such that the vowels never occupy the even places?

ATQ, The word 'STRIVE' has 6 letters: S, T, R, I, V, E Vowels = I, E (2 vowels) Consonants = S, T, R, V (4 consonants) Total positions = 6 (1, 2, 3, 4, 5, 6) Even places = 2nd, 4th, 6th (3 places) Odd places = 1st, 3rd, 5th (3 places) Condition: Vowels never occupy even places, so vowels must occupy odd places. Number of ways to arrange 2 vowels in 3 odd places = 3P2 Or, 3P2 = 3! / (3 - 2)! = 6 Remaining 4 positions are to be filled by 4 consonants. Number of ways to arrange 4 consonants = 4! Or, 4! = 24 Total arrangements = 6 × 24 So, Total arrangements = 144 Hence, the correct answer is A.