jmc

There are $\left(\genfrac{}{}{0ex}{}{52}{3}\right)=22,100$ ways to choose 3 cards out of 52, without regard to order. To choose two cards of matching rank, there are 13 different ranks and $\left(\genfrac{}{}{0ex}{}{4}{2}\right)=6$ combinations of suits to choose from, for a total of $13\times 6=78$ different possibilities. There are 48 remaining cards not in the same rank as the first two. This means there are $78\times 48=3,744$ ways to choose a hand that is a pair. So the probability that a randomly drawn hand is a pair is $\frac{3744}{22100}=\boxed{\frac{72}{425}}$.