How many permutations of all the letters in the word ARMADILLO begin with letter A?

Question

I know that there are 9 total letters and there are three A`s and two L`s. Is the answer just $9!/(3!*2!)$? Thanks for any help.

Answer 1

$9!/(3!\cdot 2!)$ would be the total number of words you can make with all the letters, with no restriction on order. Since the first letter has to be an A, we only have 8 letters to work with, and only 1 repeat letter (2 L's).
The answer should be 8!/2!

Answer 2

Fix the A in the beginning and you're left with $8$ letters to permute with. Since L occurs twice, the number of permutations are $\dfrac{8!}{2!}$.