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Question
A and B draw two cards each, one after another, from a pack of well-shuffled pack of 52 cards. The probability that all the four cards drawn are of the same suit is
Options
\[\frac{44}{85 \times 49}\]
\[\frac{11}{85 \times 49}\]
\[\frac{13 \times 24}{17 \times 25 \times 49}\]
none of these
Solution
\[ \frac{44}{85 \times 49}\]
\[\text{ Total cards } = 52\]
\[\text{ There are four suits of cards in a pack, i.e. diamond, heart, spade and club } .\]
\[P\left( \text{ all 4 cards are of same suit } \right) = P\left( \text{ all 4 cards are of diamond } \right) + P\left( \text{ all 4 cards are of heart } \right) + P\left( \text { all 4 cards are of spade }\right) + P\left( \text{ all 4 cards are of club } \right)\]
\[ = 4 \times \frac{13}{52} \times \frac{12}{51} \times \frac{11}{50} \times \frac{10}{49}\]
\[ = 4 \times \frac{11}{85 \times 49}\]
\[ = \frac{44}{85 \times 49}\]
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