jmc

There are two cases.

Case 1: The first card is a $♡$ but not a 10.

The probability of the first card satisfying this is $\frac{12}{52},$ and then the probability that the second card is a 10 is $\frac{4}{51}.$

Case 2: The first card is the 10 $♡$.

The probability of the first card being the 10 $♡$ is $\frac{1}{52},$ and then the probability that the second card is a 10 is $\frac{3}{51}.$

We then add the probability of the two cases (since they are exclusive) to get $$\frac{12}{52}\times \frac{4}{51}+\frac{1}{52}\times \frac{3}{51}=\boxed{\frac{1}{52}}.$$