Question

Three cards are drawn from a pack of 52 cards. Find the chance that they are a king, a queen, and a jack

Answer 1

3 cards can be drawn from a pack of 52 cards in ⁵²C₃ ways.

∴ n(S) = ⁵²C₃

Let event D: The cards drawn are a king, a queen, and a jack.

There are 4 kings, 4 queens, and 4 jacks in a pack of 52 cards.

∴ 1 king can be drawn from 4 kings in ⁴C₁ ways,

1 queen can be drawn from 4 queens in ⁴C₁ ways and

1 jack can be drawn from 4 jacks in ⁴C1 ways.

∴ n(D) = ⁴C₁ × ⁴C₁ × ⁴C₁ = 4 × 4 × 4

∴ P(D) = `("n"("D"))/("n"("S"))`

= `(4 xx 4 xx 4)/(""^52"C"_3)`

= `(4 xx 4 xx 4)/((52 xx 51 xx 50)/(3 xx 2 xx 1)`

= `16/5525`