What is the probability of having a king and a queen when two cards are drawn from a pack of 52 cards ?

Options

A. `16/663`
B. `2/663`
C. `4/663`
D. `8/663`

Explanation

To find the probability of drawing one king and one queen when two cards are drawn from a standard deck of 52 cards, we can follow these steps:

### Step 1: Determine the total number of ways to draw 2 cards from 52 cards.
The total number of ways to choose 2 cards from 52 is given by the combination formula:

\[ \text{Total ways} = \binom{52}{2} = \frac{52 \times 51}{2} = 1326 \]

### Step 2: Determine the number of favorable outcomes for drawing one king and one queen.
To have one king and one queen, we can choose:
- 1 king from the 4 kings available.
- 1 queen from the 4 queens available.

The number of ways to choose 1 king from 4 is:

\[ \binom{4}{1} = 4 \]

The number of ways to choose 1 queen from 4 is:

\[ \binom{4}{1} = 4 \]

Thus, the total number of favorable outcomes for drawing one king and one queen is:

\[ \text{Favorable outcomes} = \binom{4}{1} \times \binom{4}{1} = 4 \times 4 = 16 \]

### Step 3: Calculate the probability.
The probability \( P \) of drawing one king and one queen is given by the ratio of the number of favorable outcomes to the total outcomes:

\[ P(\text{one king and one queen}) = \frac{\text{Favorable outcomes}}{\text{Total ways}} = \frac{16}{1326} \]

### Step 4: Simplify the fraction.
To simplify \( \frac{16}{1326} \):

\[ P = \frac{16}{1326} = \frac{8}{663} \]

### Final Answer:
The probability of drawing one king and one queen when two cards are drawn from a pack of 52 cards is:

\[ \frac{8}{663} \]

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