In how many different ways can the letters of the word 'DANCING' be arranged in such a way that the vowels always come together? Choose the correct option.
A) A)360  B) B)480  C) C)720  D) D)1440  E) of these
The word 'DANCING' has 7 different letters.   When the vowels AI are always together, they can be supposed to form one letter.   Then, we have to arrange the letters DNCNG (AI).   Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.   The vowels (EAI) can be arranged among themselves in 2! = 2 ways.   Required number of ways = (720 x 2) = 1440.   ANSWER:1440
<result>D</result>
In how many different ways can the letters of the word 'DANCING' be arranged in such a way that the vowels always come together?