In how many different ways can the letters of the word 'SENDING' be arranged in such a way that the vowels always come together?
Choices
A) A)360  B) B)480  C) C)720  D) D)5040  E) of these
The word 'SENDING' has 7 different letters.   When the vowels EI are always together, they can be supposed to form one letter.   Then, we have to arrange the letters SNDNG (EI).   Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.   The vowels (EI) can be arranged among themselves in 2! = 2 ways.   Required number of ways = (720 x 2) = 1440.   ANSWER:480
<result>B</result>
In how many different ways can the letters of the word 'SENDING' be arranged in such a way that the vowels always come together?