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In how many different ways can the letters of the word 'LEADING'  be arranged in such a way that the vowels always come together?

In how many different ways can the letters of the word 'LEADING'  be arranged in such a way that the vowels always come together? Correct Answer 720

Calcuation:

The word 'LEADING' has 7 different letters

When the vowels EAI are always together, they can be supposed to form one letter

Then, we have to arrange the letters LNDG (EAI)

Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways

The vowels (EAI) can be arranged among themselves in 3! = 6 ways

Required number of ways = (120 x 6)

⇒ 720

∴ Required number of ways is 720

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