please help

SAMBHRANT

 

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.