How many random 3 letter words have exactly 1 "A"? No repetitions. Trying to build intuition here

Question

I think the options are either:

c(3,1) * c(25,2) (as in, choose 1 of the three letters to be the “A” and choose 2 of the remaining 25 letters for the other one) = 900

OR

if the first letter is an A, then there are 25 options for the second and 24 for the third. There are 3 slots for the A, so 25*24*3 = 1800

Are either correct? If so, what’s the intuition around why 1 is wrong?

Answer 1

You forgot to permute the two remaining letters in the first approach. They will permute in $2!$ ways, so the total ways will be multiplied by $2!$.