What percent of the different arrangements of the letters of the word ABACUS are those in which the vowels appear together? Choose one:  A) 10%  B) 20%  C) 40%  D) 50%  E) 60%
The total number of different arrangements are 6!/2=360. We divide here by 2, since we have two same letters A.   Letters A, A, and U are vowels. Put them together and consider as one object. So, we have 4 different objects (AAU) B C S. The number of different arrangements of them are 4!=24. And we have 3 possibilities to arrange vowels: AAU, AUA, UAA. Therefore, we have 24*3= 
<gadget id="calculator">24*3</gadget>
<output>72</output>
72 different arrangements.   Hence, 72/360*100%=20%.   The correct answer is 20%.
<result>B</result>
What percent of the different arrangements of the letters of the word ABACUS are those in which the vowels appear together?