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

Answer 1

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`