P(X=1). = (4c1)*(48c1)/(52c2).  ( Choose one card of the 4 aces and other one from the remaining 48 cards)

P(X=2). = (4c2)*(4/(52c2).  Choose two from 4 aces.

Where c standard notation.

The total number of ways in which two cards can be drawn from the deck of 52 card is 52C2

Number of ways in which one is an Ace and other is not an Ace is 4C1*48C1

Number of ways in which both in the cards are Ace are 4C2.

Therefore the required probability is (4C2 + 4C1 x 48C1)/52C2.

Hope this helps