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Arrange the letters of the word 'SEQUENCE' such that the vowels always appear together.
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Solution: Step 1: Identify vowels: E, E, E (3 vowels) Step 2: Treat vowels as single unit: [EEE] + 5 consonants = 6 units Step 3: Arrange 6 units: 6! / 3! (for repeated E) Step 4: Arrange vowels internally: 3! / 3! (identical vowels) Step 5: Total = (6! / 3!) * (3! / 3!) = 120 Step 6: Correct calculation: Treat [EEE] as 1 unit, 5 consonants + 1 unit = 6! Step 7: Correct internal arrangement: 3!/3! = 1 Step 8: Final calculation: 6!/3! = 72 ways
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