In how many ways can the letters of the word APPEAR be rearranged such that the vowels always appear together? Choose the correct answer:
A) 6!/2!
B) 3!*3!
C) 4!/2!
D) 4! *3!/(2!*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 APPEAR be rearranged such that the vowels always appear together   = (4! * 3! )/2!*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 AND 2 elements of consonant group are identical we divide by 2! 2! .   The entire vowel group is considered as a single group .   Answer 4! *3!/(2!*2!)
<result>D</result>
In how many ways can the letters of the word APPEAR be rearranged such that the vowels always appear together?