jmc

Because there are 5 teachers on the committee, there are 6 non-teachers. Now, in total, we can form $\left(\genfrac{}{}{0ex}{}{11}{4}\right)=330$ subcomittees. The number of subcommittees with zero non-teachers is the number of subcommittees formed by the 5 teachers, totaling $\left(\genfrac{}{}{0ex}{}{5}{4}\right)=5$. So, the number of subcomittees with at least one non-teacher is $330-5=\boxed{325}$.