Three cards are drawn at random one after another from an ordinary pack of…
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Three cards are drawn at random one after another from an ordinary pack of cards. Find the probability that they will consist of a king, a queen and an ace.
- A.
48/14785
- B.
16/5525
- C.
22/8750
- D.
154/23584
Attempted by 18 students.
Show answer & explanation
Correct answer: B
Key idea: compute the probability for one specific order and then multiply by the number of possible orders.
Probability for a specific order (king then queen then ace): (4/52) × (4/51) × (4/50).
Number of possible orders of the three ranks: 3! = 6.
Total probability = 6 × (4/52) × (4/51) × (4/50) = 384/132600 = 16/5525.
Therefore the probability that the three drawn cards consist of a king, a queen and an ace (in any order) is 16/5525.