Permutations

Using all the letters from A, B, C, E , F, F, G. How many 7 letter permutations are there if the first letter has to be a consonant.

My work:

Total 7 letter permutations are 7! / 2! = 2520 since there are 2 Fs

Number of permutations that start with either A or E:

There are two options for the first letter (A or E) and there are 6!/2! ways to arrange the other 6 letters so that they are after the first letter.

So the number of permutations that start with either A or E = 2*6!/2! = 720

My answer = 2520-720 = 1800

Is my answer correct?

5*6*5*4*3*2*1 = 30*120 = 3600, except that we can't tell the difference between the two "F"s, so 3600 / 2 = 1800. There it is.