Three cards are drawn one by one without replacement from a well shuffled pack of 52 cards. Find the probability that the first two cards drawn are queen and third card drawn is a king.

Explanation

To solve the problem of finding the probability that the first two cards drawn are queens and the third card drawn is a king, we can break it down into a series of steps.

### Step-by-Step Solution:

1. **Determine the total number of cards and specific cards**:
- In a standard deck, there are 52 cards, which include 4 queens and 4 kings.

2. **Calculate the probability of drawing the first queen**:
- The probability \( P_1 \) of drawing a queen first:
\[ P_1 = \frac{\text{Number of Queens}}{\text{Total Cards}} = \frac{4}{52} = \frac{1}{13} \]

3. **Calculate the probability of drawing the second queen**:
- After drawing the first queen, there are now 51 cards left, including 3 queens.
- The probability \( P_2 \) of drawing a second queen:
\[ P_2 = \frac{\text{Remaining Queens}}{\text{Remaining Total Cards}} = \frac{3}{51} = \frac{1}{17} \]

4. **Calculate the probability of drawing a king as the third card**:
- After drawing two queens, there are now 50 cards left, including 4 kings.
- The probability \( P_3 \) of drawing a king:
\[ P_3 = \frac{\text{Number of Kings}}{\text{Remaining Total Cards}} = \frac{4}{50} = \frac{2}{25} \]

5. **Calculate the total probability of the sequence**:
- The total probability of drawing a queen, then another queen, and then a king is the product of the individual probabilities:
\[ P = P_1 \times P_2 \times P_3 = \frac{1}{13} \times \frac{1}{17} \times \frac{2}{25} \]
- Calculating this gives:
\[ P = \frac{1 \times 1 \times 2}{13 \times 17 \times 25} = \frac{2}{5525} \]

### Final Answer:
The probability that the first two cards drawn are queens and the third card drawn is a king is:
\[ \frac{2}{5525} \]