Two cards are drawn from a pack of well shuffled cards. Find the probability that one is a club and other in King

Let X be the event that cards are in a club which is not king and other is the king of club.
Let Y be the event that one is any club card and other is a non-club king.
Hence, required probability:
=P(A)+P(B)

= $\frac{12C1*1C1}{52C2}+\frac{13C1*3C1}{52C2}$

= $12*\frac{2}{52*51}+13*3*\frac{2}{52*51}$=  $\frac{24+78}{52*51}$ =  $\frac{1}{26}$