Question

Two cards are drawn at random from a standard pack of \(52\) cards. Then the probability that the draw consists of exactly one face card and exactly one ace card is...

• A. \(\frac{7}{221}\)
• B. \(\frac{5}{221}\)
• C. \(\frac{8}{221}\)
• D. \(\frac{9}{221}\)

Hint:

Count favourable pairs and divide by $\binom{52}{2}$.

Answer 1

The Correct Option is C

Step 1: Sequential method
Face then ace: $\frac{12}{52}\cdot\frac{4}{51}$. Ace then face: $\frac{4}{52}\cdot\frac{12}{51}$.
Sum $=\frac{96}{2652}=\frac{8}{221}$.

Final Answer:
Option (C). \[ \boxed{\text{(C)}} \]