Question

4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?

Answer 1

Number of ways of drawing 4 cards from 52 cards =  ⁵²C₄
In a deck of 52 cards, there are 13 diamonds and 13 spades.

∴ Number of ways of drawing 3 diamonds and one spade =  ¹³C₃  x  ¹³C₁

Thus, the probability of obtaining 3 diamonds and one spade =¹³C₃ x ¹³C₁ / ⁵²C₄