How many words can be formed by using all letters of the word ‘DAUGHTER’ so that the vowels always come together?
Select the correct option.
A) 1214  B) 4320  C) 1254  D) 3265  E) 4512
Given word contains 8 different letters. When the vowels AUE are always together, we may suppose them to form an entity, treated as one letter.   Then, the letters to be arranged are DGNTR (AUE).   Then 6 letters to be arranged in 6p6 = 6! = 720 ways.   The vowels in the group (AUE) may be arranged in 3! = 6 ways.   Required number of words = (720x6) = 4320.   Ans: 4320
<result>B</result>
How many words can be formed by using all letters of the word ‘DAUGHTER’ so that the vowels always come together?