Question

Two cards are drawn from a pack of 52 cards. Find the probability that both are face cards.

Answer 1

Two cards can be drawn from a pack of 52 cards in ⁵²C₂ ways.
∴ n(S) = ⁵²C₂
Let D be the event that both the cards drawn are face cards.

There are 12 face cards in a pack of 52 cards.
∴ 2 face cards can be drawn from 12 face cards in ¹²C₂ ways
∴ n(D) = ¹²C₂

∴ P(D) = `("n"("D"))/("n"("S"))`

= `(""^12"C"_2)/(""^52"C"_2)`