Question

PLEASE HELP FAST!!

In poker, a 5-card hand is called two pair if there are two cards of one rank, two cards of another rank, and a fifth card of a third rank. (For example, QQ668 is two pair.) The order of the cards doesn't matter (so, for example, QQ668 and 68QQ6 are the same). How many 5-card hands are two pair? (Assume a standard 52-card deck with 13 ranks in each of 4 suits.)

Answer 1

one way of counting:
select three different values. (M ways to do so)
choose which ones are pairs (N ways to do so)
answer: \(M \times N\).
use binomial coefficients.

Answer 2

Can you explain further?

Answer 3

\(\binom nk\) is the number of ways to select k elements from a set of n elements, not taking the order into account. Use that (select 3 values from the 12 possible)

Answer 4

Hmm...ok. I think I get it now. Thanks a lot! :)

Answer 5

cool, yw

Answer 6

So the answer would be (13 pick 2)*(11 pick 1)*[(4 pick 2)*(4 pick 1)*(4 pick 1)] which would be equal to 78*11*144 which is 123552?

Answer 7

my answer would be (13 pick 3) * (3 pick 2).
how do you explain your answer?

Answer 8

We choose the two paired ranks in (13 pick 2) ways and the remaining rank in (11 pick 1) ways. Then we choose the suits for these cards in (4 pick 2)*(4 pick 2)*(4 pick 1) ways. This gives a total of 78*11*144=123552 two pair hands.

Answer 9

I think it's not correct. because I think I'm right and our two answers are different.

Answer 10

Oh OK :) No problem.

Answer 11

123552 is correct