This is the Question :

In a building there are 5 men and 5 women. we need to pick representive for the building so that at least one woman and at least one man has to be there. there are no limitions for the size of this staff (between 2 to 10 of course).
In how many ways you can choose this staff ?

Im thinking about picking 1 from the women so its 5 choose 1, the same with the men so again
5 choose 1, and then i dont care if they'll be there or not so its 2^8. 
I've been told it's not the answer but it seems so right and i have no idea why it's wrong.
Thanks in advance.