Two cards are drawn from a well-shuffled pack of $52$ cards without replacement. Then the probability that one is a red queen and other is a king of black color is $p$ then the value of $663p$ is

Since the number of red queen cards $=2$
and number of black king cards $=2$

$\therefore$ Probability that first card is red queen and other is black king
$=\frac{{}^2{C}_1}{{}^{52}{C}_1}\times \frac{{}^2{C}_1}{{}^{51}{C}_1}=\frac{1}{663}$

and probability that first card is black king and other is red queen
$=\frac{{}^2{C}_1}{{}^{52}{C}_1}\times \frac{{}^2{C}_1}{{}^{51}{C}_1}=\frac{1}{663}$

Now, required probability
$p=\frac{1}{663}+\frac{1}{663}=\frac{2}{663}$
Hence, the value of $663p$ is $2.$