[720] In how many different ways can the letters of the word LEADING be arranged in such a way that the vo

For Competitive Exams

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

360

480

720

5040

Explanation:

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.

$\therefore$ Required number of ways = $\left(120 \times 6\right)$ = 720.

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