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.