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

A. $\frac{1}{15}$

B. $\frac{25}{57}$

C. $\frac{35}{256}$

D. $\frac{1}{221}$

Solution:

Let S be the sample space

\begin{aligned} Then, n (S) =^{52} C_{2} \\ = \frac{52 \times 51}{(2 \times 1)} \\ = 1326 \end{aligned}

Let E = event of getting 2 kings out of 4

\begin{aligned} ∴ n (E) =^{4} C_{2} = \frac{4 \times 3}{2 \times 1} = 6 \\ ∴ P (E) = \frac{n (E)}{n (S)} \\ = \frac{6}{1326} \\ = \frac{1}{221} \end{aligned}

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