I wanted to have a female Trill as first officer on my ship. Since I'm playing a Cruiser, that meant Engineering Department, since that's the Commander rank slot.
However, as far as I have seen, there are just not female Trill Engineering Officers anywhere. The vendor does not sell them (at least, not at Sol or Deep Space K-7). There are none on the exchange. No one I talked to in-game has seen one.
There are a number of other combinations of department/race/gender that just do not seem to be available for Bridge Officers, as well. I am at a loss to explain what the reasoning could be not to offer all possible combinations.