Card Probability

#1
Just want to make sure what im doing is correct.

Out of a deck of 52 cards, 12 cards are selected at random w/o replacement, what is the probability of exactl 3 spades and 4 hearts ?

This is what i have so far,

((13/52)(12/51)(11/50)+(13/49)(12/48)(11/47)(10/46))/(52choose12)

But something doesnt seem right
 
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#2
OR is the correct answer as follows:

((13/52)(12/51)(11/50)(13/49)(12/48)(11/47)(10/46)/(52choose12)

OR

52c12 = possible 12 card hands
13c4=possible 4 diamonds
13c3=possible 3 heart
((13c3)(13c4))/(52c12)
 
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BGM

TS Contributor
#3
You have exactly 3 hearts and 4 spades out of 12 cards, therefore you need 5 cards from (clubs or diamonds) to fill the rest.

[math] \frac {\displaystyle \binom {13} {3} \binom {13} {4} \binom {26} {5}}
{\displaystyle \binom {52} {12}} [/math]