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probability help please :)

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Lets say you are playing poker playing against 2 other people. Everyone gets 2 cards first and your 2 cards are a pair of X's. 

5 more cards are going to come in the middle, and I want to find the probability of getting a full house. 

 

would you agree that these are the possible combinations of 5 cards?:

 

YYYKM

XYYKM

YYYKK

XYYKK

XYYYK

 

Where X is the rank of card that i have a pair of in my hand, Y, K and M is any other rank.

 

from each of those combinations i find the amount of combinations possible.

eg: for XYYKM i would do 13C1 x 2C1 x 12C1 x 4C2 x 11C2 x 4C1 x 4C1 = 1,647,360 possible combinations

 

And when i add all of them up, i would get 1,857,024.

 

Can anyone please just tell me if i am doing it correct? because i think in my answer i havent actually considered 4 cards missing from the other 2 people.

 

Thanks ;)

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