Question

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

Answer 1

Two cards can be drawn from a pack of 52 cards in ⁵²C₂ ways.
∴ n(S) = ⁵²C₂
Let G be the event that both the cards drawn are of same denominations.
A pack of cards has 13 denominations and 4 different cards for each denomination
∴ n(G) =  13 × ⁴C₂

∴ P(G) = `("n"("G"))/("n"("S")`

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