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In how many different ways can the letters of the word LEADING be arranged so that the vowels always come together?

1. 360
2. 480
3. 720
4. 5040

Correct answer: 720

Solution

LEADING has 7 distinct letters, with vowels E, A, I forming one block. So we arrange 5 units: (EAI), L, D, N, G in 5! ways, and the 3 vowels inside the block in 3! ways. Total = 5! × 3! = 720.

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