Hello, sleepywalker!

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 4differentvowels, there would be: . ways.

Since the two A's are identical, there are: . arrangements.