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### Discussion :: Permutation and Combination

1.  In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
2.  A. 360 B. 480 C. 720 D. 5040 E. None of these

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.

Required number of ways = (120 x 6) = 720.

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