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The word 'MAXIMUM' has 7 letters: 3 M's, 1 A, 1 X, 1 I, 1 U. Vowels are A, I, U (3 distinct letters). Consonants are M, X, M, M (4 letters, with M repeated 3 times). To ensure no two consonants occur together, we first arrange the vowels and then place the consonants in the gaps created by the vowels.Number of ways to arrange the 3 distinct vowels (A, I, U) is 3! = 6.These arrangements create 4 possible slots for the consonants: V_V_V.To prevent any two consonants from being together, we must place one consonant in each of these 4 slots.The consonants are M, M, M, X. The number of ways to arrange these 4 consonants in 4 distinct slots is 4! / 3! = 4.Total number of words = (ways to arrange vowels) × (ways to arrange consonants in slots) = 3! × (4! / 3!) = 6 × 4 = 24. Option (A) is 4!, which equals 24.