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?

So let me go ahead and tell you how to do this:
a) the number in the pile decreases by one each time as each card is dealt. That means: (52)x(51)x(50)x(49)x(48)= 311,875,200 different hands. 
b) each time you take out of card from the stack, the number of cards in the stack goes down, and in this case, so does the # of hearts. (14)x(13)x(12)x(11)x(48)= 1,153,152 hands can contain four hearts 
c)There are 12 face cards. Imagine removing 12 cards from the stack of 52 and setting them aside, we don't need them. You are left with 40 cards. 
(40)x(39)x(38)x(37)x(36)= 78,960,960 total possible hands 
d)So, for the total possible hands of only spades (same number will apply to clubs): (14)x(13)x(12)x(11)x(10)= 240,240 possible hands 
e) There are 28 red cards in the stack of 52. 
(28)x(27)x(26)x(25)x(24)= 11,793,600 
f)  Since there are only two, we will plug in only two numbers (twelve and eleven) for the limiting factor. (12)x(11)x(50)x(49)x(48)= 15,523,200 
g)There are 28 hearts in a stack of cards. (28)x(27)x(50)x(49)x(48)= 88,905,600 
I hope this can help

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