Question

Two cards are drawn from a pack of 52 cards. Find the probability that one is spade and other is non-spade.

Answer 1

Two cards can be drawn from a pack of 52 cards in ⁵²C₂ ways.
∴ n(S) = ⁵²C₂
Let E be the event that out of the two cards drawn one is a spade and other is non-spade.
There are 13 spade cards and 39 cards are non-spade cards in a pack of 52 cards.
∴ One spade card can be drawn from 13 spade cards in ¹³C₁ ways and one non-spade card can be drawn from 39 non-spade cards in ³⁹C₁ ways.
∴ n(E) =  ¹³C₁ × ³⁹C₁

∴ P(E) = `("n"("E"))/("n"("S")`

= `(""^13"C"_1 xx ""^39"C"_1)/(""^52"C"_2)`