From a well shuffled pack of 52 cards, three cards are drawn one by one. The probability that the three cards are Jack, Queen and King respectively?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{8}{16575}\)
The cards are drawn one by one without being put back, so after each draw the pack has one card fewer. A pack has 4 Jacks, 4 Queens and 4 Kings.
First card a Jack: \(\displaystyle\frac{4}{52}\)
Second card a Queen (51 cards left): \(\displaystyle\frac{4}{51}\)
Third card a King (50 cards left): \(\displaystyle\frac{4}{50}\)
Probability \(=\displaystyle\frac{4}{52}\times\frac{4}{51}\times\frac{4}{50}=\frac{64}{132600}=\frac{8}{16575}\)