Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:

Answer: Option D

Let S be the sample space
$$\begin{array}{rl}& n\left(S\right)={}^{52}{C}_2=\frac{52\times 51}{2\times 1}\\ & =1326\end{array}$$
Let E = event of getting 1 spade and 1 heart
∴ n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13
$$\begin{array}{rl}& ={}^{13}{C}_1{\times }^{13}{C}_1\\ & =13\times 13\\ & =169\\ & \therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{169}{1326}=\frac{13}{102}\end{array}$$