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Question
Three cards are drawn with replacement from a well shuffled pack of cards. Find the probability that the cards drawn are king, queen and jack.
Solution
\[P\left( \text{ king } \right) = \frac{4}{52}\]
\[P\left( \text{ queen } \right) = \frac{4}{52}\]
\[P\left( \text{ jack } \right) = \frac{4}{52}\]
\[\text{ These cards can be drawn in }{}^3 P_3 \text{ ways } . \]
\[P\left( \text{ king, queen and jack } \right) = \frac{4}{52} \times \frac{4}{52} \times \frac{4}{52} \times^3 P_3 \]
\[ = \frac{3!}{2197}\]
\[ = \frac{6}{2197}\]
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