Two cards are dealt from a standard deck of 52 cards.  What is the probability that the first card dealt is a $\diamondsuit$ and the second card dealt is a $\spadesuit$?
Once a $\diamondsuit$ is dealt, there are only 51 cards left in the deck, so the probability of the second card being a $\spadesuit$ is $\frac{13}{51}$, not $\frac14.$ Therefore, the probability of both cards being the required suits is $\frac14 \times \frac{13}{51} =\boxed{ \frac{13}{204}}.$