Place the seven X's in a row, inserting spaces before, after, and between them.How many arrangements are there of two A's, one E, one I and seven X's
in which no two vowels are adjacent ?
. . _ X _ X _ X _ X _ X _ X _ X _
Now we place the 4 vowels in the 8 spaces.
If we had 4 different vowels, there would be: . ways.
Since the two A's are identical, there are: . arrangements.