Two cards are drawn from a pack of 52 cards. The probability that one card is an ace and other is queen is

Options

A. `(""^(4)C_(2))/(""^(52)C_(2))`
B. `(2)/(""^(52)C_(2))`
C. `(1)/(663)`
D. `(8)/(663)`

Answer

To solve the problem of finding the probability that one card drawn is an Ace and the other is a Queen from a standard deck of 52 cards, we can follow these steps:

### Step 1: Determine the Total Number of Ways to Draw Two Cards
The total number of ways to draw 2 cards from a pack of 52 cards can be calculated using the combination formula:
\[ \text{Total ways} = \binom{52}{2} = \frac{52 \times 51}{2} = 1326 \]

### Step 2: Determine the Number of Favorable Outcomes
To find the number of favorable outcomes where one card is an Ace and the other is a Queen, we can choose:
- 1 Ace from the 4 available Aces: \(\binom{4}{1} = 4\)
- 1 Queen from the 4 available Queens: \(\binom{4}{1} = 4\)

Thus, the total number of favorable outcomes is:
\[ \text{Favorable outcomes} = \binom{4}{1} \times \binom{4}{1} = 4 \times 4 = 16 \]

### Step 3: Calculate the Probability
The probability of drawing one Ace and one Queen can be calculated using the formula:
\[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{16}{1326} \]

### Step 4: Simplify the Probability
Now, we simplify the fraction:
\[ \frac{16}{1326} = \frac{8}{663} \]

### Final Answer
Thus, the probability that one card is an Ace and the other is a Queen is:
\[ \frac{8}{663} \]

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