Question

Three cards are drawn from a pack of 52 cards. Find the chance that all are from the same suit

Answer 1

3 cards can be drawn from a pack of 52 cards in ⁵²C₃ ways.

∴ n(S) = ⁵²C₃

Let event C: All the cards drawn are from the same suit.

A pack of 52 cards consists of 4 suits each containing 13 cards.

∴ 3 cards can be drawn from the same suit in ¹³C₃

∴ n(C) = ¹³C₃ × 4

∴ P(C) = `("n"("C"))/("n"("S"))`

= `(4 xx ""^13"C"_3)/(""^52"C"_3)`

= `(4 xx 13 xx 12 xx 11)/(52 xx 51 xx 50)`

= `22/425`