How many words can be formed from the letters of the word ‘DIRECTOR’ So that the vowels are always together?  Choose the correct choice from the following answers:
A) 3251
B) 2160
C) 1203
D) 2564
E) 5421
In the given word, we treat the vowels IEO as one letter.   Thus, we have DRCTR (IEO).   This group has 6 letters of which R occurs 2 times and others are different.   Number of ways of arranging these letters = 6!/2! = 360.   Now 3 vowels can be arranged among themselves in 3! = 6 ways.   Required number of ways = (360x6) = 2160.   Ans: 2160
<result>B</result>
How many words can be formed from the letters of the word ‘DIRECTOR’ So that the vowels are always together?