Five cards are dealt form 52. a) How many different hands can be dealt? b) How many hands will contain 4 hearts? c) How many hands will contain no face cards? d) How many hands will contain only spades or only clubs? e) How many hands will contain only red cards? f) How many will contain no more than 2 face cards? g) How many will contain at least 2 hearts?

Question

Five cards are dealt form 52.   a) How many different hands can be dealt? b) How many hands will contain 4 hearts? c) How many hands will contain no face cards? d) How many hands will contain only spades or only clubs? e) How many hands will contain only red cards? f) How many will contain no more than 2 face cards? g) How many will contain at least 2 hearts?

anonymous · Answer

just to clarify.....i'm really just not certain whether to use nCr or just like, 52x51....etc.. :S

anonymous · Answer

that is because you can do it either way. it is a matter of preference, what you find easier

anonymous · Answer

First one is 52C5 (you could get to the same thing from first principle as well)

anonymous · Answer

52C5 = 2598960
52*51*50*49*48= 311,875200

anonymous · Answer

that's what's messing me up..thank you!!

anonymous · Answer

ok i made a slight misinterpretation of your question. i thought it was asking for probabilities, and in that case you have a choice
as estudier says, first one is 52 choose 5

anonymous · Answer

okay- thanks!! :D

anonymous · Answer

second one is 13 choose 4 times 39 choose 1

anonymous · Answer

are the rest clear?

anonymous · Answer

yes, I think I've got them now. just was uncertain which method to use. thank you both!