Computing number of ways for two pair in five card stud

I am trying to compute the number of ways to get two pair in game of 5 card stud. My answer is as follows, but I think there is a mistake somewhere in my counting. Can someone tell me where I am going wrong?

There are 13 ways to choose the denomination for the first pair and 12 ways to choose the denomination for the second pair. Once the denominations are chosen there are 4 choose 2 ways to choose the suits for the first pair and 4 choose 2 ways to choose the suit for the second pair. The last card can be any of the 52-8 = 44 cards left that are not the same denomination as the pairs. 44*13*12*(4 choose 2)^2 = 247104.

Quote: CsMajor219

There are 13 ways to choose the denomination for the first pair and 12 ways to choose the denomination for the second pair.

but order of the pairs do not matter so divide by 2! (2*1)

how about C(13,2) for the ranks

C(4,2)^2 for the suits

C(44,1) for the 5th card

78*36*44 =123,552 = number of ways
C(52,5) = 2,598,960
probability about 0.047539016 or 1 in 21

Sally

Quote: CsMajor219

I am trying to compute the number of ways to get two pair in game of 5 card stud. My answer is as follows, but I think there is a mistake somewhere in my counting. Can someone tell me where I am going wrong?

There are 13 ways to choose the denomination for the first pair and 12 ways to choose the denomination for the second pair. Once the denominations are chosen there are 4 choose 2 ways to choose the suits for the first pair and 4 choose 2 ways to choose the suit for the second pair. The last card can be any of the 52-8 = 44 cards left that are not the same denomination as the pairs. 44*13*12*(4 choose 2)^2 = 247104.

Close. The difference is that the order of the denominations (ranks) of the first and second pair doesn't matter. So, it should be 44*(13 choose 2)*(4 choose 2)^2.

Quote: CrystalMath

Close. The difference is that the order of the denominations (ranks) of the first and second pair doesn't matter. So, it should be 44*(13 choose 2)*(4 choose 2)^2.

calculating the number of permutations 13*12 would be correct where order does matter
but of course combinations work swell for this

Thanks for the replies, so I'm overcounting by a factor of 2! Because the order the ranks are picked doesnt matter if I'm understanding correctly.