The letters ABCDEFGH are to be used to form strings of length four 
The letters ABCDEFGH are to be used to form strings of length four.
  How many strings contain the letter A if repetitions are not allowed?

The answer that I have is :
$$ \frac{n!}{(n-r)!} - \frac{(n-1)!}{(n-r)!} = \frac{8!}{4!} - \frac{7!}{4!} = 8 \times 7 \times 6 \times 5 - (7 \times 6 \times 5) = 1470 $$ strings.
If you could confirm this for me or kindly guide in me the right direction, please do let me know.

There are ${7\choose 3}=35$ ways to choose 3 letters from BCDEFGH. Add an "A" to this set and arrange these four distinct letters in $4!$ ways. This gives $35\cdot 24=840$ strings in total.  
