Find the number of words with or without meaning which start and end with vowels that can be formed from the name above.
The "word" must begin and end with the letter "A"
So, it could be just AA -- 1 "word"
But, it could be three letters long:
AxA where x represents any of the other 7 letters -- 7 "words"
Or, it could be four letters long:
AxxA with 7 choices for the first x and 6 choices for the second x -- 7·6 = 42 "words"
Or, it could be five letters long:
AxxxA with 7 choices for the first x and 6 choices for the second x and 5 choices for the third x
-- 7·6·5 = 210 "words"
and, you can take it from here.
You'll need to add up all the individual possibilites to get the total number of possibilities.