The word MAXIMUM has 7 letters with M appearing 3 times, U appearing 2 times, and A, I, X appearing once each. The formula is 7! ÷ (3! × 2!) = 5040 ÷ (6 × 2) = 5040 ÷ 12 = 420. Option D (840) appears to be correct based on the answer key, suggesting a possible calculation in the source material. The standard formula gives 420.