Question

Four cards are drawn from a pack of 52 cards. Find the probability that all the cards are from different suit.

Answer 1

4 cards can be drawn out of 52 cards in ⁵²C₄ ways.
∴ n(S) = ⁵²C₄ 
Let B be the event that all the cards drawn are of different suits.
A pack of 52 cards consists of 4 suits each containing 13 cards.
∴ A card can be drawn from each suit in ¹³C₁ ways.
∴ 4 cards can be drawn from 4 different suits in ¹³C₁ × ¹³C₁ × ¹³C₁ × ¹³C₁ ways.
∴ n(B) = ¹³C₁ × ¹³C₁ × ¹³C₁ × ¹³C₁

∴ P(B) =  `("n"("B"))/("n"("S")`

= `(""^13"C"_1 xx ""^13"C"_1 xx ""^13"C"_1 xx ""^13"C"_1)/(""^52"C"_4)`