jmc

There are 5 ways to choose a Republican, 6 ways to choose a Democrat, and 2 ways to choose an Independent for a total of $5\times 6\times 2=60$ different subcommittees of a Republican, Democrat, and Independent. There are $\left(\genfrac{}{}{0ex}{}{13}{3}\right)=\frac{13\cdot 12\cdot 11}{3\cdot 2\cdot 1}=286$ ways to choose 3 people from 13 to form a committee, so there are 286 possible committees. Therefore, the probability that the subcommittee is made up of a Republican, Democrat, and Independent is $\frac{60}{286}=\boxed{\frac{30}{143}}$ .