Arranging a word This is the question :
In how many ways you can arrange the word AAABBCDEFG so that the first letter is A or E ?
I'm not sure if im doing this right. My plan is to take all the arrangments and reduce < br>
the number of options where A is the first letter and than reducing the options where 
E is the first letter and thus getting :
$$\frac{10!}{3!2!} -  \frac{7\cdot 9!}{3!2!} - \frac{9!}{3!2!}$$
sorry about the formating, still new at this, hope it's clear.
Thanks in advance

Here's another possibility:
Choose $6$ positions for BBCDFG, but excluding the first position.  ($9\choose 6$ ways.)
Arrange BBCDFG in these $6$ chosen positions: ($\frac{6!}{2}$ ways.)
Arrange AAAE in three remaining positions ($4$ ways.)
Total: $84\cdot 360\cdot 4=120960$ arrangements.
