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.
Best Answer
Fix A first, then the then you have $7$ choices for the remaining $3$ places, then number of possible arrangements: $$7 \times 6 \times 5$$
Now there are exactly $4$ places where the that A possible fit, making the total number of possible arrangements as: $$7 \times 6 \times 5 \times 4 = 840$$