Question 1191840
<pre>
Choose an arrangement of the three vowels {E,A,U} in 3! ways. 

Let X represent the arrangement of {E,A,U} that you chose.

For each of those possible 3! choices of vowel arrangement, 
we can choose an arrangement of {B,X,T,Y} any of 4! ways.

Answer: (3!)(4!)

Edwin</pre>