In how many ways can the letters of the word SPECULATION be arranged such that all the vowels always appear together?  Choose the correct choice from the following choices: A) 6!*5! B) 7!*5! C) 11! D) 11!*6! E) 11!*5!
The 11 letters can be grouped into 6 consonants and one set of 5 vowels.   The number of ways to arrange 7 units is 7!   Then, for each arrangement, the 5 vowels can be arranged in 5! ways.   The total number of arrangements is 7!*5!   The answer is 7!*5!.
<result>B</result>
In how many ways can the letters of the word SPECULATION be arranged such that all the vowels always appear together?