Two pairs

Probability Level 4

Hi,

I am trying to calculate the number of hands in Poker with two pairs. For the first pair, I got 13 times the number of combinations of four in two and for the second pair I got 12 times the number of combinations of four in two. However, I cannot get properly the combination for the isolated card of the hand. Please, help me.


The answer is 123552.

Paul Romero by Paul Romero , 50, USA

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1 solution

Patrick Chatain
Apr 20, 2020

Choose the two pairs as ( 13 2 ) \binom{13}{2} . For each pair we have ( 4 2 ) \binom{4}{2} suit combinations. For the last card we have 11 11 choices and 4 4 choices of suit. So we have ( 13 2 ) ⋅ ( 4 2 ) 2 ⋅ 11 ⋅ 4 = 123552 \binom{13}{2} \cdot \binom{4}{2}^2 \cdot 11 \cdot 4 = 123552 combinations.

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