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Question
Two cards are drawn from a pack of 52 cards. Find the probability that one is a face card and the other is an ace card
Solution
Two cards can be drawn from a pack of 52 cards in 52C2 ways.
∴ n(S) = 52C2
Let event A: Out of the two cards drawn, one is a face card and the other is an ace card.
There are 12 face cards and 4 ace cards in a pack of 52 cards
∴ One face card can be drawn from 12 face cards in 12C1 ways and one ace card can be drawn from 4 ace cards in 4C1 ways.
∴ n(A) = 12C1 × 4C1
∴ P(A) = `("n"("A"))/("n"("S"))`
= `(""^12"C"_1 xx ""^4"C"_1)/(""^52"C"_2)`
= `(12 xx 4)/((52 xx 51)/(2 xx 1)`
= `8/221`
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