Question

Four cards are drawn from a pack of 52 cards. Find the probability that all cards are club and one of them a jack.

Answer 1

4 cards can be drawn out of 52 cards in ⁵²C₄ ways.
∴ n(S) = ⁵²C₄
Let D be the event that all the 4 cards drawn are clubs and one of them is a jack.
In a pack of 52 cards, there are 13 club cards having 1 jack card.
∴ 1 jack can be drawn in ¹C₁ way and the other 3 cards can be drawn from the remaining 12 club cards in ¹²C₃ ways.
∴ n(D) = ¹C₁ × ¹²C₃

∴ P(D) = `("n"("D"))/("n"("S"))`

= `(""^12"C"_3xx""^1"C"_1)/(""^52"C"_4)`