An experiment consists of dealing 8 cards from a standard 52- card deck. What is the probability of being dealt 8 hearts?

**Solution:-**

P(E) =

Let the sample space S be the set of all 8-card hands that could be selected from a 52-card deck. Since the order in a hand does not matter, the number of possible selections is C_{52,8}.

The number of element in S is

n(s) = C_{52,8 }= 752538150

Let the event E be the set of all 8-card hands that could be selected from the 13 hearts in the deck. Again , the order does not matter so the number of possible selection is c_{13,8}. The number of element in E is n(E) = c_{13,8} = 1287

Thus , the probability of being dealt 8 hearts is

0.000002