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In how many ways can the letters of the word DRAUGHT be arranged, if the vowels are always kept together?

In how many ways can the letters of the word DRAUGHT be arranged, if the vowels are always kept together? Correct Answer 1440

Calculation:

The word 'DRAUGHT'  has 7 different letters.

When the vowels AU are kept together, they can be supposed to form one letter.

Then, we have to arrange the letters DRGHT (AU).

Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 ways

The vowels (AU) can be arranged among themselves in 2! = 2 × 1 = 2 ways

∴ Required number of ways = 720 × 2 ⇒ 1440 

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