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GATE 2016 ME (ME3) – Question 39

Engineering Mathematics · Probability and Statistics: Probability, conditional probability, sampling theorems · 2 marks · Multiple choice

Three cards were drawn from a pack of 52 cards. The probability that they are a king, a queen, and a jack is

  1. 16/5525
  2. 64/2197
  3. 3/13
  4. 8/16575

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Correct answer: (A) 16/5525

Explanation

There are C(52,3)=22100 equally likely unordered hands. Favourable hands select one of four cards of each rank, giving4³=64. Probability64/22100=**16/5525, A**. No extra factorial is needed because both counts are unordered.