Question

From a pack of 52 cards, 3 cards are drawn at random. What is the probability that one is an ace, one is a queen, and one is a jack?

• A. \( \frac{19}{5525} \)
• B. \( \frac{21}{5525} \)
• C. \( \frac{17}{5525} \)
• D. \( \frac{16}{5525} \)

Hint:

Use combinations for drawing specific cards from a deck. Multiply individual selections and divide by total combinations.

Answer 1

The Correct Option is D

Number of ways to choose: - 1 ace from 4: \( ^4C_1 = 4 \) - 1 queen from 4: \( ^4C_1 = 4 \) - 1 jack from 4: \( ^4C_1 = 4 \) Total favorable outcomes = \( 4 \cdot 4 \cdot 4 = 64 \) Total ways to choose any 3 cards from 52: \[ ^{52}C_3 = \frac{52 \cdot 51 \cdot 50}{3 \cdot 2 \cdot 1} = 22100 \Rightarrow \text{Probability} = \frac{64}{22100} = \frac{16}{5525} \]