How many ways are there to select a committee of $17$ politicians chosen from a room full of indistinguishable Democrats, indistinguishable republicans, and indistinguishable Independents if every party must have at least two members on the committee? If, in addition, no group may have a majority of the committee members?

I was able to find the number of ways to select a committee if each party must have at least two members on the committee: $\binom{11+2}{2}=\binom{13}{2}=78$ ways. 

I am confused on the second part of the problem. 

Any help is appreciated.