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?

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.