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Question
Two cards are drawn from a pack of 52 cards. Find the probability that both are diamonds.
Solution
Two cards can be drawn from a pack of 52 cards in 52C2 ways.
∴ n(S) = 52C2
Let B be the event that both the cards drawn are diamond.
There are 13 diamond cards in a pack of 52 cards.
∴ 2 diamond cards can be drawn from 13 diamond cards in 13C2 ways
∴ n(B) = 13C2
∴ P(B) = `("n"("B"))/("n"("S"))`
= `(""^13"C"_2)/(""^52"C"_2)`
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