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 $= \space^{52}C_4$
In a deck of 52 cards, there are 13 diamonds and 13 spades.

∴ Number of ways of drawing 3 diamonds and one spade =$^{13}C_3\times ^{13}C_1$
Thus, the probability of obtaining 3 diamonds and one spade =$\frac{^{13}C_3\times^{13}C_1}{^{52}C_4}.$