Multiple choice

Three cards are drawn at random from a well-shuffled deck of cards. What is the probability of drawing a king, a queen, and a jack?

  1. $\frac{16}{5525}$
  2. $\frac{64}{5225}$
  3. $\frac{16}{225}$
  4. $\frac{4}{525}$

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A standard deck has 52 cards with 4 kings, 4 queens, and 4 jacks. We need to draw one king, one queen, and one jack in any order. Number of ways to choose the specific cards: 4C1 × 4C1 × 4C1 = 4 × 4 × 4 = 64. These 3 cards can be arranged in 3! = 6 orders (KQJ, KJQ, QKJ, QJK, JQK, JKQ). Total favorable = 64 × 6 = 384. Total ways to draw any 3 cards from 52 = 52C3 = 52×51×50/(3×2×1) = 22100. Probability = 384/22100 = 16/5525. Option A is correct.

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