In how many ways can the letters of the word SPHERICAL be arranged such that all the vowels always appear together? Options.
A) 9!*6!  B) 9!  C) 7!*3!  D) 9!*3!  E) 6!*3!
The 9 letters can be grouped into 6 consonants and one set of 3 vowels.   The number of ways to arrange 7 units is 7!   Then, for each arrangement, the 3 vowels can be arranged in 3! ways.   The total number of arrangements is 7!*3!   The answer is 7!*3!.
<result>C</result>
In how many ways can the letters of the word SPHERICAL be arranged such that all the vowels always appear together?