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Question
Three cards are drawn with replacement from a well shuffled pack of 52 cards. Find the probability that the cards are a king, a queen and a jack.
Solution
\[P\left( \text{ king } \right) = P\left( A \right) = \frac{4}{52}\]
\[P\left( \text { queen } \right) = P\left( B \right) = \frac{4}{52}\]
\[P\left( \text{ jack } \right) = P\left( C \right) = \frac{4}{52}\]
\[P\left( \text{ king, queen and jack } \right) = 3! \times P\left( A \right) \times P\left( B \right) \times P\left( C \right) \]
\[ = 3 \times 2 \times \frac{4}{52} \times \frac{4}{52} \times \frac{4}{52}\]
\[ = \frac{6}{2197}\]
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