# Card Probability

#### ITman95

##### New Member
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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#### ITman95

##### New Member
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
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.

$\frac {\displaystyle \binom {13} {3} \binom {13} {4} \binom {26} {5}} {\displaystyle \binom {52} {12}}$

#### ITman95

##### New Member
Alright, Thanks for the help at least i was close sort of...i wasnt sure about (26c5)