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Question
Two cards are drawn from a pack of 52 cards. Find the probability that both are from the same suit.
Solution
Two cards can be drawn from a pack of 52 cards in 52C2 ways.
∴ n(S) = 52C2
Let event C: Both the cards are drawn are of the same suit.
A pack of 52 cards consists of 4 suits each containing 13 cards.
∴ 2 cards can be drawn from the same suit in 13C2 ways.
∴ n(C) = 13C2 × 4
∴ P(C) = `("n"("C"))/("n"("S"))`
= `(4 xx ""^13"C"_2)/(""^52"C"_2)`
= `(4 xx 13 xx 12)/(52 xx 51)`
= `12/51`
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