jmc

Because there are 4 teachers on the committee, there are 6 non-teachers. Now, in total, we can form $\left(\genfrac{}{}{0ex}{}{10}{4}\right)=210$ subcomittees. The number of subcomittees with 0 teachers is the number of subcommittees formed by the 6 nonteachers, totaling $\left(\genfrac{}{}{0ex}{}{6}{4}\right)=15$. So, the number of subcomittees with at least 1 teacher is $210-15=\boxed{195}$.