The word  WASTEFUL  has 8 ubique letters, there is no repetition of letters.



(a)  In (a), in each of 7 position can be any of 8 letters, 
     
     so the answer in this case is   = 2097152.



(b)  In (b), in the 1st position can be any of 8 letters;
             in the 2nd position can be any of remaining 7 letters
                    . . . and so on . . . 
     
     So the answer in this case is  8*7*6*5*4*3*2 = 40320.

     It is the product of 7 consecutive integer numbers in descending order, starting from 8.