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Permutation and Combination - General Aptitude

Q1:

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

A 360

B 480

C 720

D 5040

E None of these

ANS:C - 720

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.