Drawing two aces with and without putting back

Two cards are drawn from a standard $52$-card deck. Find the probability that both are aces (a) if the first card is returned and the deck reshuffled before the second draw, and (b) if the first card is kept out.

(a) $1/169$; (b) $1/221$. With replacement each draw is an ace with probability $\tfrac1{13}$, so $\tfrac1{169}$. Without replacement it is $\tfrac4{52}\cdot\tfrac3{51}=\tfrac1{221}$.