All of the diamonds have been removed from a deck of card.You are dealt five cards. What is the probability that you are dealt a full house? Can someone explain why in the answer in the back of the book there is a two multiplying the answer in the numerator? I got [(3C3)(13C1)(3C2)(12C1)]/[(52C5)]
christinetat: Feb. 8, 2015, 9:59 p.m.
The numerator is correct, but the denominator should be (39C5); since all the diamonds have been removed, 13 cards are gone from the total deck, so it is (52-13)C5
AshleyChang: Feb. 8, 2015, 11:29 p.m.
I got the same answer as you! I just calculated it, and it is the same as the answer in the back of the book. I think the 2 is there because for the solution in the book, the two values are being chosen at once rather than separately. Since one of them is doubled and the other is tripled, order matters; the 2 serves to make sure that there are two different cases if one number goes from tripled-->doubled and vice versa...I think that's how it works. Sorry for the confusing explanation!