From a standard 52card deck what is the probability of being

From a standard 52-card deck, what is the probability of being dealt (a) 5 black cards? (b) 5 hearts?

Solution

Total cards = 52

a) Total black cards = 26

So, P(5 black cards) = 26C5 / 52C5

                                  = 65780 / 2598960

                                  = 0.025

b) total hearts = 13

So, P(5 hearts) = 13C5 / 52C5

                          = 1287 / 2598960

                          = 0.0005