jmc

There are a total of $\left(\genfrac{}{}{0ex}{}{8}{4}\right)=70$ combinations of socks. We seek combinations that have one pair of socks with the same color and two separate socks with different colors for a total of three colors. There are $\left(\genfrac{}{}{0ex}{}{4}{3}\right)$ ways to choose three colors. From each combination of three colors, there are $\left(\genfrac{}{}{0ex}{}{3}{1}\right)$ ways to choose a color for the only pair of socks. There are 2 socks to choose from for each of the colors that only appear once among the four socks she chooses. Therefore, there are $\left(\genfrac{}{}{0ex}{}{4}{3}\right)\left(\genfrac{}{}{0ex}{}{3}{1}\right)\cdot 2\cdot 2=48$ ways to choose an appropriate combination of socks. The probability of choosing such a combination is $\frac{48}{70}=\boxed{\frac{24}{35}}$.