From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

Answer: Option D

Let S be the sample space
$$\begin{array}{rl}& \text{Then},n\left(S\right)={}^{52}{C}_2\\ & =\frac{52\times 51}{\left(2\times 1\right)}\\ & =1326\end{array}$$
Let E = event of getting 2 kings out of 4
$$\begin{array}{rl}& \therefore n\left(E\right)={}^4{C}_2=\frac{4\times 3}{2\times 1}=6\\ & \therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ & =\frac{6}{1326}\\ & =\frac{1}{221}\end{array}$$