Question

What is the theoretical probability of being dealt exactly three 4s in a 5-card hand from a standard 52-card deck? ~~ I understand how to do combinations but this confuses me a lot.. Can someone explain?

Answer 1

There are 4 C 3 = 4 ways to be dealt three "4" cards

You have 2 card slots left. You can't be dealt another "4" card because then you wouldn't have exactly three "4" cards. So you will will have 52-4 = 48 cards left to choose from. So you will have 48 C 2 = 1128 different ways to pick another 2 cards


This is all out of 52 C 5 = 2,598,960 ways of picking 5 cards out of 52

Answer 2

So to sum up, you have

4*1128 = 4512

ways of getting the hands that you want and this is out of 2,598,960 ways total

Answer 3

Oh that makes more sense. Thanks for your help !

Answer 4

np