Question

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

Answer 1

Two cards can be drawn from a pack of 52 cards in ⁵²C₂ ways.
∴ n(S) = ⁵²C₂
Let B be the event that both the cards drawn are diamond.
There are 13 diamond cards in a pack of 52 cards.
∴ 2 diamond cards can be drawn from 13 diamond cards in ¹³C₂ ways
∴ n(B) = ¹³C₂

∴ P(B) = `("n"("B"))/("n"("S"))`

= `(""^13"C"_2)/(""^52"C"_2)`