jmc

Since her friends' birthdays are completely independent of her own, each of them has a $\frac{1}{7}$ probability of being born on a Tuesday, and a $1-\frac{1}{7}=\frac{6}{7}$ probability of not being born on a Tuesday. If exactly 2 friends were born on a Tuesday, the probability of this occurring is $\left(\genfrac{}{}{0ex}{}{3}{2}\right)\cdot \frac{1}{7}\cdot \frac{1}{7}\cdot \frac{6}{7}=3\cdot \frac{6}{343}=\boxed{\frac{18}{343}}$.