In how many ways can the letters of the word EMULATION be arranged such that all the vowels always appear together? Pick
A) 9! B) 9!*4! C) 5!*4! D) 9!*5! E) 5!*5!
The 9 letters can be grouped into 4 consonants and one set of 5 vowels.   The number of ways to arrange 5 units is 5!   Then, for each arrangement, the 5 vowels can be arranged in 5! ways.   The total number of arrangements is 5!*5!   The answer is 5!*5!.
<result>E</result>
In how many ways can the letters of the word EMULATION be arranged such that all the vowels always appear together?