In how many ways can the letters of the word REGULATION be arranged such that all the vowels always appear together?
Choose one:
A) 10!*5!  B) 10!*6!  C) 10!  D) 6!*5!  E) 5!*5!
The 10 letters can be grouped into 5 consonants and one set of 5 vowels.   The number of ways to arrange 6 units is 6!   Then, for each arrangement, the 5 vowels can be arranged in 5! ways.   The total number of arrangements is 6!*5!   The answer is 6!*5!.
<result>D</result>
In how many ways can the letters of the word REGULATION be arranged such that all the vowels always appear together?