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Question
Three cards are drawn from a pack of 52 cards. Find the chance that two are queen cards and one is an ace card
Solution
3 cards can be drawn from 52 cards in 52C3 ways.
∴ n(S) = 52C3
Let event A: Out of the three cards drawn, 2 are queens and 1 is an ace card.
There are 4 queens and 4 aces in a pack of 52 cards.
∴ 2 queens can be drawn from 4 queens in 4C2 ways and 1 ace can be drawn out of 4 aces in 4C1 ways.
∴ n(A) = 4C2 × 4C1
∴ P(A) = `("n"("A"))/("n"("S"))` = `(""^4"C"_2 xx ""^4"C"_1)/(""^52"C"_3)`
= `((4xx3)/(2) xx 4)/((52xx51xx50)/(3xx2xx1))`
= `6/5525`
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