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In how many ways can the letters of the word 'EXAMPLE' be arranged so that all vowels are together?
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Solution: Step 1: Identify vowels and consonants in 'EXAMPLE' (E, A, E) and (X, M, P, L)
Step 2: Treat the group of vowels (EAE) as a single unit
Step 3: Arrange 5 units (EAE, X, M, P, L) in 5! ways = 120
Step 4: Arrange vowels (EAE) internally in 3!/2! ways (due to repeated E) = 3
Step 5: Total arrangements = 120 * 3 = 360
Step 6: Correct option is not listed, verify original problem constraints