Five cards are drawn simultaneously from a pack of 52 playing cards. What is the probability of drawing 2 cards of hearts and 3 black cards?

As the cards are drawn simultaneously, there is no replacement made. Let S be the sample space and E1 be the event of selecting 2 hearts and E2 be the event of selecting 3 black cards. Number of ways of drawing 5 cards out of 52= n(S) = ⁵²C₅ Number of ways of drawing 2 hearts out of 13 = n(E1) = ¹³C₂ Number of ways of drawing 3 black out of 26 = n(E2) = ²⁶C₃ Since both the events are independent of each other, then the probability of drawing 2 hearts and 3 black cards = P(E) = n(E1)x n(E2)/n(S) = (¹³C₂)x(²⁶C₃) / (⁵²C₅ )