In how many ways can the letters of the word ACTUAL be rearranged such that the vowels always appear together? Select.
A) 6!/2!  B) 3!*3!  C) 4!/2!  D) (4! *3!)/2!  E) 3!*3!/2
In the word ABACUS , there are 3 vowels - 2 A's and U   Number of ways the letters of word ACTUAL be rearranged such that the vowels always appear together   = (4! * 3! )/2!   We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .   The entire vowel group is considered as a single group .   Answer (4! *3!)/2!
<result>D</result>
In how many ways can the letters of the word ACTUAL be rearranged such that the vowels always appear together?