Question

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

Answer 1

Two cards can be drawn from a pack of 52 cards in ⁵²C₂ ways
∴ n(S) = ⁵²C₂
Let F be the event that both the cards drawn are of the same suit.
A pack of 52 cards consists of 4 suits each containing 13 cards.
2 cards can be drawn from a suit in ¹³C₂ ways.
A suit can be selected in 4 ways.
∴ n(F) = ¹³C₂ × 4

∴ P(F) = `("n"("F"))/("n"("S"))`

= `(4xx""^13"C"_2)/(""^52"C"_2)`